financial derivatives
TRANSCRIPT
A derivative is a financial instrument that derives or gets it value from some real good or stock. It is in its most basic form simply a contract between two parties to exchange value based on the action of a real good or service. Typically, the seller receives money in exchange for an agreement to purchase or sell some good or service at some specified future date.
In finance, a derivative is a financial instrument (or, more simply, an agreement between two parties) that has a value, based on the expected future price movements of the asset to which it is linked—called the underlying asset—[1] such as a share or a currency. The term `Derivative' indicates that it has no independent value, i.e. its value isentirely `derived' from the value of the underlying asset. The underlying asset can besecurities, commodities, bullion, currency, livestock or anything else. In other words,derivative means a forward, future, option or any other hybrid contract of pre-determined fixed duration, linked for the purpose of contract fulfillment to the valueof a specified real or financial asset or to an index of securities. There are many kinds of derivatives, with the most common beingswaps, futures, and options. Derivatives are a form of alternative investment.
Definition of Financial Derivatives
Section 2(ac) of Securities Contract Regulation Act (SCRA) 1956 defines Derivative as:a) “a security derived from a debt instrument, share, loan whether secured or unsecured, riskinstrument or contract for differences or any other form of security;b) “a contract which derives its value from the prices, or index of prices, of underlying securities”.
Underlying Asset in a Derivatives Contract
As defined above, the value of a derivative instrument depends upon the underlying asset. The Underlying asset may assume many forms:i. Commodities including grain, coffee beans, orange juice;ii. Precious metals like gold and silver;iii. Foreign exchange rates or currencies;iv. Bonds of different types, including medium to long term negotiable debt securities issued bygovernments, companies, etc.v. Shares and share warrants of companies traded on recognized stock exchanges and Stock Indexvi. Short term securities such as T-bills; andvii. Over- the Counter (OTC)2 money market products such as loans or deposits.
Derivatives are used by investors to:
provide leverage (or gearing), such that a small movement in the underlying
value can cause a large difference in the value of the derivative;
speculate and make a profit if the value of the underlying asset moves the
way they expect (e.g., moves in a given direction, stays in or out of a
specified range, reaches a certain level);
hedge or mitigate risk in the underlying, by entering into a derivative
contract whose value moves in the opposite direction to their underlying
position and cancels part or all of it out;
obtain exposure to the underlying where it is not possible to trade in the
underlying (e.g., weather derivatives);
create option ability where the value of the derivative is linked to a specific
condition or event (e.g., the underlying reaching a specific price level).
The need for a derivatives marketThe derivatives market performs a number of economic functions:1. They help in transferring risks from risk averse people to risk oriented people2. They help in the discovery of future as well as current prices3. They catalyze entrepreneurial activity4. They increase the volume traded in markets because of participation of risk averse people in greater numbers5. They increase savings and investment in the long run
Derivatives Products Traded in Derivatives Segment of NSE NSE started trading in index futures, based on popular S&P CNX Index, on
June 12, 2000 as its first derivatives product. Trading on index options was introduced on June 4,
2001. Futures on individual securities started on November 9, 2001. The futures contracts are available on 2338 securities stipulated by the Securities & Exchange Board of India (SEBI). Trading in options on individual securitiescommenced from July 2, 2001. The options contracts are American style and cash settled and are available on 233 securities. Trading in interest rate futures was introduced on 24 June 2003 but it was closed subsequently due to pricing problem. The NSE achieved another landmark in product introduction by launching Mini Index Futures & Options with a minimum contract size of Rs 1 lac.
NSE crated history by launching currency futures contract on US Dollar-Rupee on August 29, 2008 in Indian Derivatives market. Table 3 presents a description of the types of products traded at F& O segment of NSE.( As Traded on May 29, 2009. Chhota SENSEX was launched on January 1, 2008. With a small or 'mini' market lot of 5, it allows for comparatively lower capital outlay, lower trading costs, more precise hedging and flexible trading. It is a step to encourage and enable small investors to mitigate risk and enable easy access to India's most popular index, SENSEX, through futures & options)
Development of derivatives market in India
The first step towards introduction of derivatives trading in India was the promulgation of the Securities Laws(Amendment) Ordinance, 1995, which withdrew the prohibition on options in securities. The market for derivatives, however, did not take off, as there was no regulatory framework to govern trading of derivatives. SEBI set up a 24–member committee under the Chairmanship of Dr.L.C.Gupta on November 18, 1996 to develop appropriate regulatory framework for derivatives trading in India. The committee submitted its report on March 17, 1998 prescribing necessary pre–conditions for introduction of derivatives trading in India. The committee recommended that derivatives should be declared as ‘securities’ so that regulatory framework applicable to trading of ‘securities’ could also govern trading of securities. SEBI also set up a group in June 1998 under the Chairmanship of Prof.J.R.Varma, to recommend measures for risk containment in derivatives market in India. The report, which was submitted in October 1998, worked out the operational details of margining system, methodology for charging initial margins, broker net worth, deposit requirement and real–time monitoring requirements.
The Securities Contract Regulation Act (SCRA) was amended in December 1999 to include derivatives within the ambit of ‘securities’ and the regulatory framework was developed for governing derivatives trading. The act also made it clear that derivatives shall be legal and valid only if such contracts are traded on a recognized stock exchange, thus precluding OTC derivatives. The government also rescinded in March 2000, the three–decade old notification, which prohibited forward trading in securities.
Derivatives trading commenced in India in June 2000 after SEBI granted the finalapproval to this effect in May 2001. SEBI permitted the derivative segments of two stock exchanges, NSE and BSE, and their clearing house/corporation to commence trading and settlement in approved derivatives contracts. To begin with, SEBI approved trading in index futures contracts based on S&P CNX Nifty and BSE–30(Sensex) index. This was followed by approval for trading in options based on these two indexes and options on individual securities.
The trading in BSE Sensex options commenced on June 4, 2001 and the trading in options on individual securities commenced in July 2001. Futures contracts on individualstocks were launched in November 2001. The derivatives trading on NSE commenced with S&P CNX Nifty Index futures on June 12, 2000. The trading in index options commenced on June 4, 2001 and trading in options on individual securities commenced on July 2, 2001.
Single stock futures were launched on November 9, 2001. The index futures and options contract on NSE are based on S&P CNX
Trading and settlement in derivative contracts is done in accordance with the rules, By laws, and regulations of the respective exchanges and their clearing house/corporation duly approved by SEBI and notified in the official gazette. Foreign Institutional Investors(FIIs) are permitted to trade in all Exchange traded derivative products.The following are some observations based on the trading statistics provided in the NSE report on the futures and options (F&O):
Single-stock futures continue to account for a sizable proportion of the F&O
segment. It constituted 70 per cent of the total turnover during June 2002. Aprimary reason attributed to this phenomenon is that traders are comfortable withsingle-stock futures than equity options, as the former closely resembles theerstwhile badla system.
On relative terms, volumes in the index options segment continues to remain poor.This may be due to the low volatility of the spot index. Typically, options areconsidered more valuable when the volatility of the underlying (in this case, theindex) is high. A related issue is that brokers do not earn high commissions byRecommending index options to their clients, because low volatility leads to higher Waiting time for round-trips.
•Put volumes in the index options and equity options segment have increased since January 2002. The call-put volumes in index options have decreased from 2.86 in January 2002 to 1.32 in June. The fall in call-put volumes ratio suggests that the Traders are increasingly becoming pessimistic on the market.
• Farther month futures contracts are still not actively traded. Trading in equity options on most stocks for even the next month was non-existent.
• Daily option price variations suggest that traders use the F&O segment as a less risky alternative (read substitute) to generate profits from the stock price movements. The fact that the option premiums tail intra-day stock prices is evidence to this. Calls on Satyam fall, while puts rise when Satyam falls intra-day. If calls and puts are not looked as just substitutes for spot trading, the intra-day. Stock price variations should not have a one-to-one impact on the option premiums.
Applications of Financial DerivativesSome of the applications of financial derivatives can be enumerated as follows:1. Management of risk: This is most important function of derivatives. Risk management is not about the elimination of risk rather it is about the management of risk. Financial derivatives provide a powerful tool for limiting risks that individuals and organizations face in the ordinary conduct of their businesses. It requires a thorough understanding of the basic principles that regulate the pricing of financial derivatives. Effective use of derivatives can save cost, and it can increase returns for the organisations.2. Efficiency in trading : Financial derivatives allow for free trading of risk components and that leads to improving market efficiency. Traders can use a position in one or more financial derivatives as a substitute for a position in the underlying instruments. In many instances, traders find financial derivatives to be a more attractive instrument than the underlying security. This is mainly because of the greater amount of liquidity in the market offered by derivatives as well as the lower transaction costs associated with trading a financial derivative as compared to the costs of trading the underlying instrument in cash market.3. Speculation : This is not the only use, and probably not the most important use, of financial derivatives. Financial derivatives are considered to be risky. If not used properly, these can leads to financial destruction in an organisation like what happened in Barings Plc. However, these instruments act as a powerful instrument
for knowledgeable traders to expose themselves to calculated and well understood risks in search of a reward, that is, profit.4. Price discover : Another important application of derivatives is the price discovery which means revealing information about future cash market prices through the futures market. Derivatives markets provide a mechanism by which diverse and scattered opinions of future are collected into one readily discernible number which provides a consensus of knowledgeable thinking.5. Price stabilization function : Derivative market helps to keep a stabilising influence on spot prices by reducing the short-term fluctuations. In other words, derivative reduces both peak and depths and leads to price stabilisation effect in the cash market for underlying asset.
Classification of DerivativesBroadly derivatives can be classified in to two categories as shown in Fig.1: Commodity derivatives and financial derivatives. In case of commodity derivatives, underlying asset can be commodities like wheat, gold, silver etc., whereas in case of financial derivatives underlying assets are stocks, currencies, bonds and other interest rates bearing securities etc. Since, the scope of this case study is limited to only financial derivatives so we will confine our discussion to financial derivatives only.
Figure 1: Classification of Derivatives
Commodity
derivatives
Financial
Forward ContractA forward contract is an agreement between two parties to buy or sell an asset at a specified point of time in the future. In case of a forward contract the price which is paid/ received by the parties is decided at the time of entering into contract. It is the simplest form of derivative contract mostly entered by individuals in day to day’s lifeForward contract is a cash market transaction in which delivery of the instrument is deferred until the contract has been made. Although the delivery is made in the future, the price is determined on the initial trade date. One of the parties to a forward contract assumes a long position (buyer) and agrees to buy the underlying asset at a certain future date for a certain price. The other party to the contract known as seller assumes a short position and agrees to sell the asset on the same date for the same price. The specified price is referred to as the delivery price. The contract terms like delivery price and quantity are mutually agreed upon by the parties to the contract.No margins are generally payable by any of the parties to the other. Forwards contracts are traded over-the- counter and are not dealt with on an exchange unlike futures contract. Lack ofliquidity and counter party default risks are the main drawbacks of a forward contract. For instance, consider a US based company buying textile from an exporter from England worth £ 1 million payment due in 90 days. The Importer is short of Pounds- it owes pounds for future delivery. Suppose the spot (cash market) price of pound is US $ 1.71 and importer fears that in next 90 days, pounds might rise against the dollar, thereby raising the dollar cost of the textiles. The importer can guard against this risk by immediately negotiating a 90 days forward contract with City Bank at a forward rate of say, £ 1= $1.72. According to the forward contract, in 90 days the City Bank will give the US Importer £ I million (which it will use to pay for textile order), and importer will give the bank $ 1.72 million (1million ×$1.72) which is the dollar cost of £ I million at the forward rate of $ 1.72.
Futures ContractFutures is a standardized forward contact to buy (long) or sell (short) the underlying asset at a specified price at a specified future date through a specified exchange. Futures contracts are traded on exchangesthat work as a buyer or seller for the counterparty. Exchange sets the standardized terms in term of Quality, quantity, Price quotation, Date and Delivery place (in case of commodity).The features of afutures contract may be specified as follows:i) These are traded on an organised exchange like IMM, LIFFE, NSE, BSE, CBOT etc.ii) These involve standardized contract terms viz. the underlying asset, the time of maturity and the manner of maturity etc.iii) These are associated with a clearing house to ensure smooth functioning of the market.iv )There are margin requirements and daily settlement to act as further safeguard.
Complex instruments Basic instruments
Forward Futures Options Swaps Leaps Swapations Exotic
v) These provide for supervision and monitoring of contract by a regulatory authority.vi) Almost ninety percent future contracts are settled via cash settlement instead of actual delivery of underlying asset. Futures contracts being traded on organized exchanges impart liquidity to the transaction. The clearinghouse, being the counter party to both sides of a transaction, provides a mechanism that guarantees the honouring of the contract and ensuring very low level of default (Hirani, 2007).Following are the important types of financial futures contract:-i )Stock Future or equity futures,ii )Stock Index futures,iii )Currency futures, andiv) interest Rate bearing securities like Bonds, T- Bill Futures. To give an example of a futures contract, suppose on November 2007 Ramesh holds 1000 shares of ABC Ltd. Current (spot) price of ABC Ltd shares is Rs 115 at National Stock Exchange (NSE). Ramesh entertains the fear that the share price of ABC Ltd may fall in next two months resulting in a substantial loss to him. Ramesh decides to enter into futures market to protect his position at Rs 115 per share for delivery in January 2008. Each contract in futures market is of 100 Shares. This is an example of equity future in which Ramesh takes short position on ABC Ltd. Shares by selling 1000 shares at Rs 115 and locks into future price.
Options ContractIn case of futures contact, both parties are under obligation to perform their respective obligations out of a contract. But an options contract, as the name suggests, is in some sense, an optional contract. An option is the right, but not the obligation, to buy or sell something at a stated date at a stated price. A “call option” gives one the right to buy; a “put option” gives one the right to sell. Options are the standardized financial contract that allows the buyer (holder) of the option, i.e. the right at the cost of option premium, not the obligation, to buy (call options) or sell (put options) a specified asset at a setprice on or before a specified date through exchanges.Options contracts are of two types: call options and put options. Apart from this, options can also be classified as OTC (Over the Counter) options and exchange traded options. In case of exchange traded options contract, contracts are standardized and traded on recognized exchanges, whereas OTC options are customized contracts traded privately between the parties. A call options gives the holder (buyer/one who is long call), the right to buy specified quantity of the underlying asset at the strike price on or before expiration date. The seller (one who is short call) however, has the obligation to sellthe underlying asset if the buyer of the call option decides to exercise his option to buy.Suppose an investor buys One European call options on Infosys at the strike price of Rs. 3500 at a premium of Rs. 100. Apparently, if the market price of Infosys on the day of expiry is more than Rs. 3500, the options will be exercised. In contrast, a put options gives the holder (buyer/ one who is long put), the right to sell specified quantity of the underlying asset at the strike price on or before an expiry date. The seller of the put options (one who is short put) however, has the obligation to buy the underlying asset at the strike price if the buyer decides to exercise his option to sell. Right to sell is called a Put Options. Suppose X has 100 shares of Bajaj Auto
Limited. Current price (March) of Bajaj auto shares is Rs 700 per share. X needs money to finance its requirements after two months which he will realize after selling 100 shares after two months. But he is of the fear that by next two months price of share will decline. He decides to enter into option market by buying Put Option (Right to Sell) with an expiration date in May at a strike price of Rs 685 per share and a premium of Rs 15 per shares.
Swaps ContractA swap can be defined as a barter or exchange. It is a contract whereby parties agree to exchange obligations that each of them have under their respective underlying contracts or we can say, a swap is an agreement between two or more parties to exchange stream of cash flows over a period of time in the future. The parties that agree to the swap are known as counter parties. The two commonly usedswaps are:
i) Interest rate swaps which entail swapping only the interest related cash flows between the parties in the same currency, and
ii) Currency swaps: These entail swapping both principal and interest between the parties, with the cash flows in one direction being in a different currency than the cash flows in the opposite direction.Other types of derivatives:
Warrants: Options generally have lives of upto one year, the majority of options traded onoptions exchanges having a maximum maturity of nine months. Longer-dated options arecalled warrants and are generally traded over-the-counter.LEAPS: The acronym LEAPS means Long-Term Equity Anticipation Securities. These areoptions having a maturity of upto three years.Baskets: Basket options are options on portfolios of underlying assets. The underlyingasset is usually a moving average or a basket of assets. Equity index options are a form ofbasket options.Swaptions: Swaptions are options to buy or sell a swap that will become operative at theexpiry of the options. Thus a swaption is an option on a forward swap. Rather than havecalls and puts, the swaptions market has receiver swaptions and payer swaptions. Areceiver swaption is an option to receive fixed and pay floating. A payer swaption is an
option to pay fixed and receive floating.
Participants in Derivatives Market1. Hedgers: They use derivatives markets to reduce or eliminate the risk associated with price of an asset. Majority of the participants in derivatives market belongs to this category.2. Speculators : They transact futures and options contracts to get extra leverage in betting on future movements in the price of an asset. They can increase both the potential gains and potential losses by usage of derivatives in a speculative venture.3. Arbitrageurs: Their behaviour is guided by the desire to take advantage of a discrepancy between prices of more or less the same assets or competing assets in different markets. If, for example, they see the futures price of an asset getting out of line with the cash price, they will take offsetting positions in the two markets to lock in a profit.
introduction to Derivatives (unit 2)
A Derivative is an instrument whose value is derived from the value of underlying
assets, which may be commodities, foreign exchange, bonds, stocks or even
stocks indices, etc. For example, in the case of a rice derivative, say ‘rice
futures,’ the underlying asset is rice, which is a commodity. The value of ‘rice
futures’ will be derived from the current price of rice. Similarly, in the case of
'index futures,' say NSE Index Futures, the NSE Index (the nifty) is the underlying
asset.
Forward Contracts
In a forward contract, two parties agree to do a trade at some future date, at a
stated price and quantity. However, no money is exchanged.
Forward markets worldwide are cited by several problems:-
Lack of centralized trading.
Illiquidity.
Counter party Risk and Exposure.
Future Basics
Future Contracts
A "futures" contract is an exchange traded forward contract to buy or sell a pre-
determined quantity of an asset on a pre-determined future date at a pre-
determined price. Contracts are standardized and there’s centralized trading
ensuring liquidity.
They encompass the sale of financial instruments or physical commodities for
future delivery. Futures contracts try to predict what the value of an index or
commodity will be at some date in the future. The futures contract will state the
price that will be paid and the date of delivery.
Futures contracts are marked to market each day at their end-of-day settlement
prices, and the resulting daily gains and losses are passed through to the gaining
or losing accounts. Futures contracts can be terminated by an offsetting
transaction (i.e., an equal and opposite transaction to the one that opened the
position) executed at any time prior to the contract's expiration. The vast majority
of futures contracts are terminated by offset or a final cash payment rather than by
delivery.
Trading in futures originated from Japan during the 18th century
and was primarily used for the trading of rice and silk. It wasn't until the 1850s
that the U.S. started using futures markets for grain and other agriculture entities.
Futures on financial instruments came much later
Features of Future Contracts
Contract Guarantee: Guaranteed by the clearinghouse of the exchange on
which the contracts are executed.
Cash Flows: Futures contracts require daily payments of profits and losses.
Contract Terms: All terms except for the underlying price of the commodity
are standardized.
Liquidity: Very easy to enter or exit a position because contracts are traded
on an exchange.
Process of Price Discovery
Futures prices increase or decrease largely because of the innumerable factors
that influence buyers’ and sellers’ expectations about what a particular underlying
will be worth at a given time in the future. As new supply and demand
developments occur and as more current information becomes available, these
judgments are reassessed and the price of a particular futures contract may be
bid upward or downward. This process of reassessment of price discovery is
continuous.
On any given day the price of a July futures contract will reflect the consensus of
buyers’ and sellers’ current opinions about what the value of the
underlying(index/stock/commodity) will be when the contract expires in July. As
new or more accurate information becomes available or as expectations change,
the July futures price may in-crease or decrease
Applications of futures: Hedging Speculation Risk management
Basic Positions
There are two positions that you can take in a futures contract:
Long- this is when you buy a futures contract, and agree to receive delivery of the underlying asset (stocks/indices/commodities).
For e.g.: If you buy a Satyam Computers 26jun2003 futures contract, then you have agreed to accept the delivery of the underlying asset at the agreed price on the expiration date.
Short- this is when you sell a futures contract, and agree to make delivery of the underlying asset (stocks/indices/commodities).
For e.g.: If you sell a Satyam Computers 26 jun 2003 futures contract, thenyou have agreed to make the delivery of the underlying asset at the agreed price on the expiration
date.
In India, we have two type of equity futures: -
Index Futures
Individual Stock/Equity Futures
Index Futures
An index future is a derivative whose value is derived from the value of the
underlying asset (e.g. S&P CNX NIFTY, BSE Sensex). While trading on index
futures, the investors are basically buying and selling the basket of securities
comprising the index in their relative weights. Index Future contracts are settled
in cash.
Individual Stock/Equity Futures
A stock future is a derivative whose value is derived from the value of the
underlying asset (e.g. Reliance, Satyam). Stock Future contracts are settled in
cash.
Expiration Date
All Future contracts have specified date for maturity; known as expiration date. If
the last Thursday is a trading holiday, the contracts expire on the previous
trading day.
After this date, the future contracts are worthless. Future contracts have a
maximum of 3-month trading cycle - the near month (one), the next month (two)
and the far month (three). On expiry of the near month contract, new contracts
are introduced on the trading day following the expiry of the near month contract.
The new contracts are introduced for three-month duration.
In India, last Thursday of every month’s contract is taken as the expiration date
Option Contract Expiry Date
Jan 2003 30Jan2003
Feb2003 27Feb2003
March2003 27Mar2003
At any given point of time, 3-month contracts would be available for
trading. In the beginning of January; Jan, Feb and Mar future contracts are
available. After the expiry of Jan future we would have Feb, Mar and Apr
future contracts available and so on.
Size of the Futures Contract
The contract size for all futures contracts was kept at Rs 2,00,000(*as per the base price). The permitted lot size for a nifty futures contract is 200(taking the base index price as 1000).
Basic Trading Strategies
Buying (Long Position) to Profit from an Expected Price Increase
Someone expecting the price of a particular underlying to increase over a given
period of time can seek to profit bybuying futures contracts. If correct in forecasting the direction and timing of the price change, the futures contract canbe sold later for the higher price, thereby yielding a profit. If the price declines rather than increases, the trade will result in a loss.For example, assume it’s now July. The August index futures price is presently quoted at Rs1120 per unit and over the coming month you expect the price to increase. You decide to buy one August index futures contract. Further assume that by the beginning of August index futures price rise to Rs 1180 per unit and you decide to take your profit by selling. Since each contract is of 200-lot size, your Rs60 per unit profit would be Rs 12, 000 for the contract the less transaction costs.Price per unitValue of 200 lot contract JuneBuy 1 august nifty futures contractRs 1120
Rs 2, 24, 000
AugustSell 1 august nifty futures contract tRs 1180
Rs 2, 36, 000
Gain
Rs 60
Rs 12, 000*
*Excluding transaction costs
In case the futures price goes below the price at which you entered the position,
a loss would be incurred as shown in the table below: -
Price per unitValue of 200 lot contract
JuneBuy 1 august nifty futures contractRs 1120
Rs 2, 24, 000
AugustSell 1 august nifty futures contract tRs 1020
Rs 2, 04 000
Loss
Rs 100
Rs 20, 000*
*Excluding transaction costs
Selling (Short Position) to Profit from an Expected Price Decrease
Here, Instead of first buying a futures contract, you first sell a futures contract. If,
as you expect, the price does decline, a profit can be realized by later purchasing
an offsetting futures contract at the lower price. The gain per unit will be the
amount by which the purchase price is below the earlier selling price. Daily profits
or losses are credited or debited to the account in the same way.
For example, assume it’s now July. The August index futures price is presently
quoted at Rs1120 per unit and over the coming month you expect the price to
Introduction to Derivatives – I (Futures)
Jaypee Capital Services Ltd
decrease. You decide to sell one August index futures contract. Further assume
that by the beginning of August index futures price fell to Rs 1020 per unit and
you decide to take your profit by buying the futures contract. Since each contract
is of 200-lot size, your Rs100 per unit profit would be Rs 20, 000 for the contract
the less transaction costs.
Price per unitValue of 200 lot contract
JuneSell 1 august nifty futures contractRs 1120
Rs 2, 24, 000
AugustBuy 1 august nifty futures contract tRs 1020
Rs 2, 04 000
Profit
Rs 100
Rs 20, 000*
*Excluding transaction costs
In case the futures price goes above the price at which you entered the position,
a loss would be incurred as shown in the table below: -
*Excluding transaction costs
We have covered only the basic trading strategies. There are other strategies like
spreads, hedging strategies; arbitrage techniques and other advanced trading
strategies. For more information please feel free to contact us at:
Price per unitValue of 200 lot contract
JuneSell 1 august nifty futures contractRs 1120
Rs 2, 24, 000
AugustBuy 1 august nifty futures contract tRs 1180
Rs 2, 36, 000
Loss
Rs 60
Rs 12, 000*
Futures versus forwards
While futures and forward contracts are both contracts to deliver an asset on a future date at a prearranged price, they are different in two main respects:
Futures are exchange-traded, while forwards are traded over-the-counter.
Thus futures are standardized and face an exchange, while forwards are customized and face a non-exchange counterparty.
Futures are margined, while forwards are not.
Thus futures have significantly less credit risk, and have different funding.
[edit] Exchange versus OTC
Futures are always traded on an exchange, whereas forwards always trade over-the-counter, or can simply be a signed contract between two parties.
Thus:
Futures are highly standardized, being exchange-traded, whereas forwards can be unique, being over-the-counter.
In the case of physical delivery, the forward contract specifies to whom to make the delivery. The counterparty for delivery on a futures contract is chosen by the clearing house
Financial futures: A financial future is a futures contract on a short term interest rate (STIR). Contracts vary, but are often defined on an interest rate index such as 3-month sterling or US dollar LIBOR.
They are traded across a wide range of currencies, including the G12 country currencies and many others.
Some representative financial futures contracts are:
United States
90-day Eurodollar *(IMM) 1 mo LIBOR (IMM)
Fed Funds 30 day (CBOT)
As an example, consider the definition of the International Money Market (IMM) eurodollar interest rate future, the most widely and deeply traded financial futures contract.
There are four contracts per year: March, June, September, December (plus serial months)
They are listed on a 10 year cycle. Other markets only extend about 2–4 years.
Last Trading Day is the second London business day preceding the third Wednesday of the contract month
Delivery Day is cash settlement on the third Wednesday.
The minimum fluctuation (Commodity tick size) is half a basis point or 0.005%.
Payment is the difference between the price paid for the contract (in ticks) multiplied by the "tick value" of the contract which is $12.50 per tick.
Before the Last Trading Day the contract trades at market prices. The Final Settlement Price is the British Bankers Association (BBA) percentage rate for Three–Month Eurodollar Interbank Time Deposits, rounded to the nearest 1/10000th of a percentage point at 11:00 London time on that day, subtracted from 100. (Expressing financial futures prices as 100 minus the implied interest rate was originally intended to make the contract price behave similarly to a Bond price in that an increase in price corresponds to a decrease in yield).
Financial futures are extensively used in the hedging of interest rate swaps.
Characteristics of futures trading : Futures trading is unlike many other forms of investing, because one is not required to own or even buy the commodity. All that is necessary is to make a speculation on where the price of a particular commodity is going, and make a decision based on that. If an investor were speculating on crude oil, for instance, and he or she expected the price to go up in the future, that investor would buy crude oil futures contracts. And if he or she expected that the price would be going down, the investor would sell crude oil futures.
A "Futures Contract" is a highly standardized contract with certain distinct features. Some of the important features are as under :
a. Futures trading is necessarily organized under the auspices of a market association so that such trading is confined to or conducted through members of the association in accordance with the procedure laid down in the Rules & Bye-laws of the association.
b. It is invariably entered into for a standard variety known as the "basis variety" with permission to deliver other identified varieties known as "tenderable varieties".
c. The units of price quotation and trading are fixed in these contracts , parties to the contracts not being capable of altering these units.
d. The delivery periods are specified.
e. The seller in a futures market has the choice to decide whether to deliver goods against outstanding sale contracts. In case he decides to deliver goods, he can do so not only at the location of the Association through which trading is organized but also at a number of other pre-specified delivery centres.
f. In futures market actual delivery of goods takes place only in a very few cases. Transactions are mostly squared up before the due date of the contract and contracts are settled by payment of differences without any physical delivery of goods taking place.
Who trade futures?
Futures traders are traditionally placed in one of two groups: hedgers, who have an interest in the underlying asset (which could include an intangible such as an index or interest rate) and are seeking to hedge out the risk of price changes; and speculators, who seek to make a profit by predicting market moves and opening a derivative contract related to the asset "on paper", while they have no practical use for or intent to actually take or make delivery of the underlying asset. In other words, the investor is seeking exposure to the asset in a long futures or the opposite effect via a short futures contract.
g. Hedgers typically include producers and consumers of a commodity or the owner of an asset or assets subject to certain influences such as an interest rate.
h. For example, in traditional commodity markets, farmers often sell futures contracts for the crops and livestock they produce to guarantee a certain price, making it easier for them to plan. Similarly, livestock producers often purchase futures to cover their feed costs, so that they can plan on a fixed cost for feed. In modern (financial) markets, "producers" of interest rate swaps or equity derivative products will use financial futures or equity index futures to reduce or remove the risk on the swap.
i. An example that has both hedge and speculative notions involves a mutual fund or separately managed account whose investment objective is to track the performance of a stock index such as the S&P 500 stock index. The Portfolio manager often "equitizes" cash inflows in an easy and cost effective manner by investing in (opening long) S&P 500 stock index futures. This gains the portfolio exposure to the index which is consistent with the fund or account investment objective without having to buy an appropriate proportion of each of the individual 500 stocks just yet. This also preserves balanced diversification, maintains a higher degree of the percent of assets invested in the market and helps reduce tracking error in the performance of the fund/account. When it is economically feasible (an efficient amount of shares of every individual position within the fund or account can be purchased), the portfolio manager can close the contract and make purchases of each individual stock.
j. The social utility of futures markets is considered to be mainly in the transfer of risk, and increased liquidity between traders with different risk and time preferences, from a hedger to a speculator, for example
Interest rate future
An interest rate futures is a financial derivative (a futures contract) with an interest-bearing instrument as the underlying asset.
Examples include Treasury-bill futures, Treasury-bond futures and Eurodollar futures.
The global market for exchange-traded interest rate futures is notionally valued by the Bank for International Settlements at $5,794,200 million in 2005.[
Uses
Interest rate futures are used to hedge against the risk of that interest rates will move in an adverse direction, causing a cost to the company.
For example, borrowers face the risk of interest rates rising. Futures use the inverse relationship between interest rates and bond prices to hedge against the risk of rising interest rates. A borrower will enter to sell a future today. Then if interest rates rise in the future, the value of the future will fall (as it is linked to the underlying asset, bond prices), and hence a profit can be made when closing out of the future (i.e buying the future).
Treasury futures are contracts sold on the Globex market for March, June, September and December contracts. As pressure to raise interest rates rises, futures contracts will reflect that speculation as a decline in price. Price and yield will always be in an inversely correlated relationship.
Pricing of future contracts:
When the deliverable asset exists in plentiful supply, or may be freely created, then the price of a futures contract is determined via arbitrage arguments. This is typical for stock index futures, treasury bond futures, and futures on physical commodities when they are in supply (e.g. agricultural crops after the harvest). However, when the deliverable commodity is not in plentiful supply or when it does not yet exist - for example on crops before the harvest or on Eurodollar Futures or Federal funds rate futures (in which the supposed underlying instrument is to be created upon the delivery date) - the futures price cannot be fixed by arbitrage. In this scenario there is only one force setting the price, which is simple supply and demand for the asset in the future, as expressed by supply and demand for the futures contract.
Arbitrage arguments
Arbitrage arguments ("Rational pricing") apply when the deliverable asset exists in plentiful supply, or may be freely created. Here, the forward price represents the expected future value of the underlying discounted at the risk free rate—as any deviation from the theoretical price will afford investors a riskless profit opportunity and should be arbitraged away.
Thus, for a simple, non-dividend paying asset, the value of the future/forward, F(t), will be found by compounding the present value S(t) at time t to maturity T by the rate of risk-free return r.
or, with continuous compounding
This relationship may be modified for storage costs, dividends, dividend yields, and convenience yields.
In a perfect market the relationship between futures and spot prices depends only on the above variables; in practice there are various market imperfections (transaction costs, differential borrowing and lending rates, restrictions on short selling) that prevent complete arbitrage. Thus, the futures price in fact varies within arbitrage boundaries around the theoretical price.
Pricing via expectation
When the deliverable commodity is not in plentiful supply (or when it does not yet exist) rational pricing cannot be applied, as the arbitrage mechanism is not applicable. Here the price of the futures is determined by today's supply and demand for the underlying asset in the futures.
In a deep and liquid market, supply and demand would be expected to balance out at a price which represents an unbiased expectation of the future price of the actual asset and so be given by the simple relationship.
.
By contrast, in a shallow and illiquid market, or in a market in which large quantities of the deliverable asset have been deliberately withheld from market participants (an illegal action known as cornering the market), the market clearing price for the futures may still represent the balance between supply and demand but the relationship between this price and the expected future price of the asset can break down.
Relationship between arbitrage arguments and expectation:
The expectation based relationship will also hold in a no-arbitrage setting when we take expectations with respect to the risk-neutral probability. In other words: a futures price is martingale with respect to the risk-neutral probability. With this pricing rule, a speculator is expected to break even when the futures market fairly prices the deliverable commodity.
Contango and backwardation:
The situation where the price of a commodity for future delivery is higher than the spot price, or where a far future delivery price is higher than a nearer future delivery, is known as contango. The reverse, where the price of a commodity for future delivery is lower than the spot price, or where a far future delivery price is lower than a nearer future delivery, is known as backwardation.
Value at risk
In financial mathematics and financial risk management, Value at Risk (VaR) is a widely used risk measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in the portfolio) is the given probability level.[1]
For example, if a portfolio of stocks has a one-day 95% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period, assuming markets are normal and there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day in 20. A loss which exceeds the VaR threshold is termed a “VaR break.”[2]
The 5% Value at Risk of a hypothetical profit-and-loss probability density function
VaR has five main uses in finance: risk management, risk measurement, financial control, financial reporting and computing regulatory capital. VaR is sometimes used in non-financial applications as well.[3]
Important related ideas are economic capital, backtesting, stress testing, expected shortfall, and tail conditional expectation.[4]
Details:
Common parameters for VaR are 1% and 5% probabilities and one day and two week horizons, although other combinations are in use.[5]
The reason for assuming normal markets and no trading, and to restricting loss to things measured in daily accounts, is to make the loss observable. In some extreme financial events it can be impossible to determine losses, either because market prices are unavailable or because the loss-bearing institution breaks up. Some longer-term consequences of disasters, such as lawsuits, loss of market confidence and employee morale and impairment of brand names can take a long time to play out, and may be hard to allocate among specific prior decisions. VaR marks the boundary between normal days and extreme events. Institutions can lose far more than the VaR amount; all that can be said is that they will not do so very often.[6]
The probability level is about equally often specified as one minus the probability of a VaR break, so that the VaR in the example above would be called a one-day 95% VaR instead of one-day 5% VaR. This generally does not lead to confusion because the probability of VaR breaks is almost always small, certainly less than 0.5.[1]
Although it virtually always represents a loss, VaR is conventionally reported as a positive number. A negative VaR would imply the portfolio has a high probability of making a profit, for example a one-day 5% VaR of negative $1 million implies the portfolio has a 95% chance of making more than $1 million over the next day. [7]
Another inconsistency is VaR is sometimes taken to refer to profit-and-loss at the end of the period, and sometimes as the maximum loss at any point during the period. The original definition was the latter, but in the early 1990s when VaR was aggregated across trading desks and time zones, end-of-day valuation was the only reliable number so the former became the de facto definition. As people began using multiday VaRs in the second half of the 1990s they almost always estimated the distribution at the end of the period only. It is also easier theoretically to deal with a point-in-time estimate versus a maximum over an interval. Therefore the end-of-period definition is the most common both in theory and practice today.[8]
Varieties of VaR:
The definition of VaR is nonconstructive; it specifies a property VaR must have, but not how to compute VaR. Moreover, there is wide scope for interpretation in the definition.[9] This has led to two broad types of VaR, one used primarily in risk management and the other primarily for risk
measurement. The distinction is not sharp, however, and hybrid versions are typically used in financial control, financial reporting and computing regulatory capital. [10]
To a risk manager, VaR is a system, not a number. The system is run periodically (usually daily) and the published number is compared to the computed price movement in opening positions over the time horizon. There is never any subsequent adjustment to the published VaR, and there is no distinction between VaR breaks caused by input errors (including Information Technology breakdowns, fraud and rogue trading), computation errors (including failure to produce a VaR on time) and market movements.[11]
A frequentist claim is made, that the long-term frequency of VaR breaks will equal the specified probability, within the limits of sampling error, and that the VaR breaks will be independent in time and independent of the level of VaR. This claim is validated by a backtest, a comparison of published VaRs to actual price movements. In this interpretation, many different systems could produce VaRs with equally good backtests, but wide disagreements on daily VaR values.[1]
For risk measurement a number is needed, not a system. A Bayesian probability claim is made, that given the information and beliefs at the time, the subjective probability of a VaR break was the specified level. VaR is adjusted after the fact to correct errors in inputs and computation, but not to incorporate information unavailable at the time of computation.[7] In this context, “backtest” has a different meaning. Rather than comparing published VaRs to actual market movements over the period of time the system has been in operation, VaR is retroactively computed on scrubbed data over as long a period as data are available and deemed relevant. The same position data and pricing models are used for computing the VaR as determining the price movements.[2]
Although some of the sources listed here treat only one kind of VaR as legitimate, most of the recent ones seem to agree that risk management VaR is superior for making short-term and tactical decisions today, while risk measurement VaR should be used for understanding the past, and making medium term and strategic decisions for the future. When VaR is used for financial control or financial reporting it should incorporate elements of both. For example, if a trading desk is held to a VaR limit, that is both a risk-management rule for deciding what risks to allow today, and an input into the risk measurement computation of the desk’s risk-adjusted return at the end of the reporting period.[4]
VAR in Governance
An interesting takeoff on VaR is its application in Governance for endowments, trusts, and pension plans. Essentially trustees adopt portfolio Values-at-Risk metrics for the entire pooled account and the diversified parts individually managed. Instead of probability estimates they simply define maximum levels of acceptable loss for each. Doing so provides an easy metric for
oversight and adds accountability as managers are then directed to manage, but with the additional constraint to avoid losses within a defined risk parameter. VAR utilized in this manner adds relevance as well as an easy to monitor risk measurement control far more intuitive than Standard Deviation of Return. Use of VAR in this context, as well as a worthwhile critique on board governance practices as it relates to investment management oversight in general can be found in 'Best Practices in Governance".[12]
Risk measure and risk metric
The term “VaR” is used both for a risk measure and a risk metric. This sometimes leads to confusion. Sources earlier than 1995 usually emphasize the risk measure, later sources are more likely to emphasize the metric.
The VaR risk measure defines risk as mark-to-market loss on a fixed portfolio over a fixed time horizon, assuming normal markets. There are many alternative risk measures in finance. Instead of mark-to-market, which uses market prices to define loss, loss is often defined as change in fundamental value. For example, if an institution holds a loan that declines in market price because interest rates go up, but has no change in cash flows or credit quality, some systems do not recognize a loss. Or we could try to incorporate the economic cost of things not measured in daily financial statements, such as loss of market confidence or employee morale, impairment of brand names or lawsuits.[4]
Rather than assuming a fixed portfolio over a fixed time horizon, some risk measures incorporate the effect of expected trading (such as a stop loss order) and consider the expected holding period of positions. Finally, some risk measures adjust for the possible effects of abnormal markets, rather than excluding them from the computation.[4]
The VaR risk metric summarizes the distribution of possible losses by a quantile, a point with a specified probability of greater losses. Common alternative metrics are standard deviation, mean absolute deviation, expected shortfall and downside risk.[1]
VaR risk management:
Supporters of VaR-based risk management claim the first and possibly greatest benefit of VaR is the improvement in systems and modeling it forces on an institution. In 1997, Philippe Jorion wrote:[13]
[T]he greatest benefit of VAR lies in the imposition of a structured methodology for critically thinking about risk. Institutions that go through the process of computing their VAR are forced to confront their exposure to financial risks and to set up a proper risk management function. Thus the process of getting to VAR may be as important as the number itself.
Publishing a daily number, on-time and with specified statistical properties holds every part of a trading organization to a high objective standard. Robust backup systems and default assumptions must be implemented. Positions that are reported, modeled or priced incorrectly stand out, as do data feeds that are inaccurate or late and systems that are too-frequently down. Anything that affects profit and loss that is left out of other reports will show up either in inflated VaR or excessive VaR breaks. “A risk-taking institution that does not compute VaR might escape disaster, but an institution that cannot compute VaR will not.” [14]
The second claimed benefit of VaR is that it separates risk into two regimes. Inside the VaR limit, conventional statistical methods are reliable. Relatively short-term and specific data can be used for analysis. Probability estimates are meaningful, because there are enough data to test them. In a sense, there is no true risk because you have a sum of many independent observations with a left bound on the outcome. A casino doesn't worry about whether red or black will come up on the next roulette spin. Risk managers encourage productive risk-taking in this regime, because there is little true cost. People tend to worry too much about these risks, because they happen frequently, and not enough about what might happen on the worst days.[15]
Outside the VaR limit, all bets are off. Risk should be analyzed with stress testing based on long-term and broad market data.[16] Probability statements are no longer meaningful.[17] Knowing the distribution of losses beyond the VaR point is both impossible and useless. The risk manager should concentrate instead on making sure good plans are in place to limit the loss if possible, and to survive the loss if not.[1]
One specific system uses three regimes.[18]
1. One to three times VaR are normal occurrences. You expect periodic VaR breaks. The loss distribution typically has fat tails, and you might get more than one break in a short period of time. Moreover, markets may be abnormal and trading may exacerbate losses, and you may take losses not measured in daily marks such as lawsuits, loss of employee morale and market confidence and impairment of brand names. So an institution that can't deal with three times VaR losses as routine events probably won't survive long enough to put a VaR system in place.
2. Three to ten times VaR is the range for stress testing. Institutions should be confident they have examined all the foreseeable events that will cause losses in this range, and are prepared to survive them. These events are too rare to estimate probabilities reliably, so risk/return calculations are useless.
3. Foreseeable events should not cause losses beyond ten times VaR. If they do they should be hedged or insured, or the business plan should be changed to avoid them, or VaR should be increased. It's hard to run a business if foreseeable losses are orders of magnitude larger than very large everyday losses. It's hard to plan for these events, because they are out of scale with daily experience. Of course there will be unforeseeable losses more than ten times VaR, but it's pointless to anticipate them, you can't know much about them and it results in needless worrying. Better to hope that the discipline of
preparing for all foreseeable three-to-ten times VaR losses will improve chances for surviving the unforeseen and larger losses that inevitably occur.
"A risk manager has two jobs: make people take more risk the 99% of the time it is safe to do so, and survive the other 1% of the time. VaR is the border."[14]
VaR risk measurement
The VaR risk measure is a popular way to aggregate risk across an institution. Individual business units have risk measures such as duration for a fixed income portfolio or beta for an equity business. These cannot be combined in a meaningful way.[1] It is also difficult to aggregate results available at different times, such as positions marked in different time zones, or a high frequency trading desk with a business holding relatively illiquid positions. But since every business contributes to profit and loss in an additive fashion, and many financial businesses mark-to-market daily, it is natural to define firm-wide risk using the distribution of possible losses at a fixed point in the future.[4]
In risk measurement, VaR is usually reported alongside other risk metrics such as standard deviation, expected shortfall and “greeks” (partial derivatives of portfolio value with respect to market factors). VaR is a distribution-free metric, that is it does not depend on assumptions about the probability distribution of future gains and losses.[14] The probability level is chosen deep enough in the left tail of the loss distribution to be relevant for risk decisions, but not so deep as to be difficult to estimate with accuracy.[19]
Risk measurement VaR is sometimes called parametric VaR. This usage can be confusing, however, because it can be estimated either parametrically (for examples, variance-covariance VaR or delta-gamma VaR) or nonparametrically (for examples, historical simulation VaR or resampled VaR). The inverse usage makes more logical sense, because risk management VaR is fundamentally nonparametric, but it is seldom referred to as nonparametric VaR.
Mathematics:
"Given some confidence level the VaR of the portfolio at the confidence level α is given by the smallest number l such that the probability that the loss L exceeds l is not larger than (1 − α)"[3]
The left equality is a definition of VaR. The right equality assumes an underlying probability distribution, which makes it true only for parametric VaR. Risk managers typically assume that
some fraction of the bad events will have undefined losses, either because markets are closed or illiquid, or because the entity bearing the loss breaks apart or loses the ability to compute accounts. Therefore, they do not accept results based on the assumption of a well-defined probability distribution.[6] Nassim Taleb has labeled this assumption, "charlatanism."[21] On the other hand, many academics prefer to assume a well-defined distribution, albeit usually one with fat tails.[1] This point has probably caused more contention among VaR theorists than any other.9]
Criticism: VaR has been controversial since it moved from trading desks into the public eye in 1994. A famous 1997 debate between Nassim Taleb and Philippe Jorion set out some of the major points of contention. Taleb claimed VaR:[22]
1. Ignored 2,500 years of experience in favor of untested models built by non-traders2. Was charlatanism because it claimed to estimate the risks of rare events, which is
impossible
3. Gave false confidence
4. Would be exploited by traders.
HedgingHedging is a mechanism to reduce price risk inherent in open positions. Derivatives are widely used for hedging. A Hedge can help lock in existing profits. Its purpose is to reduce the volatility of a portfolio, by reducing the risk. It needs to be noted that hedging does not mean maximization of return. It only means reduction in variation of return. It is quite possible that the return is higher in the absence of the hedge, but so also is the possibility of a much lower return.
What are long/ short positions ?Long and short positions indicate whether a person has a net over-bought position (long) or over-sold position (short).
What are general hedging strategies ?
One of the popular strategies for hedging is : "If you are long in cash underlying - Short Future; and If short in cash underlying - Long Future".
This can be illustrated by a simple example. If one has bought 100 shares of say Reliance Industries and want to Hedge against market movements, he has to short an appropriate amount of Index Futures. This will reduce his overall exposure to events affecting the whole market (systematic risk). Suppose a major terrorist attack takes place, the entire market can sharply fall. In such a case, his in Reliance Industries would be offset by the gains in his short position in Index Futures.
Some other examples of where hedging strategies that can be really useful can be as follows
Reducing the equity exposure of a Mutual Fund by selling Index Futures; Investing funds raised by new schemes in Index Futures so that market exposure is
immediately taken;
Partial liquidation of portfolio by selling the index future instead of the actual shares where the cost of transaction is higher.
What is the Hedge Ratio ?The Hedge Ratio is defined as the number of Futures contracts required to buy or sell so as to provide the maximum offset of risk. This depends on the
Value of a Futures contract; Value of the portfolio to be Hedged; and
1. Sensitivity of the movement of the portfolio price to that of the Index (Called Beta).2. The Hedge Ratio is closely linked to the correlation between the asset (portfolio of
shares) to be hedged and underlying (index) from which Future is derived.
Who are Hedgers, Speculators and Arbitrageurs :
Hedgers wish to eliminate or reduce the price risk to which they are already exposed.
Speculators are those class of investors who willingly take price risks to profit
from price changes in the underlying.
Arbitrageurs profit from price differential existing in two markets by simultaneously operating in two different markets.
Hedgers, Speculators and Arbitrageurs are required for a healthy functioning of the market. Hedgers and investors provide the economic substance to any financial market. Without them the markets would lose their purpose and become mere tools of gambling. Speculators provide liquidity and depth to the market. Arbitrageurs bring price uniformity and help price discovery.The market provides a mechanism by which diverse and scattered opinions are reflected in one single price of the underlying. Markets help in efficient transfer of risk from Hedgers to speculators. Hedging only makes an outcome more certain. It does not necessarily lead to a better outcome.
Types of hedging:
The stock example above is a "classic" sort of hedge, known in the industry as a pairs trade due to the trading on a pair of related securities. As investors became more sophisticated, along with the mathematical tools used to calculate values (known as models), the types of hedges have increased greatly.
Hedging strategies
Examples of hedging include:
Forward exchange contract for currencies Currency future contracts
Money Market Operations for currencies
Forward Exchange Contract for interest (FRA)
Money Market Operations for interest
Future contracts for interest
This is a list of hedging strategies, grouped by category.
Financial derivatives such as call and put options
Risk reversal : Simultaneously buying a call option and buying a put option. This has the effect of simulating being long a stock or commodity position.
Delta neutral : This is a market neutral position that allows a portfolio to maintain a positive cash flow by dynamically re-hedging to maintain a market neutral position. This is also a type of market neutral strategy.
Natural hedges
Many hedges do not involve exotic financial instruments or derivatives such as the married put. A natural hedge is an investment that reduces the undesired risk by matching cash flows (i.e. revenues and expenses). For example, an exporter to the United States faces a risk of changes in the value of the U.S. dollar and chooses to open a production facility in that market to match its expected sales revenue to its cost structure. Another example is a company that opens a subsidiary in another country and borrows in the foreign currency to finance its operations, even though the foreign interest rate may be more expensive than in its home country: by matching the debt payments to expected revenues in the foreign currency, the parent company has reduced its foreign currency exposure. Similarly, an oil producer may expect to receive its revenues in U.S. dollars, but faces costs in a different currency; it would be applying a natural hedge if it agreed to, for example, pay bonuses to employees in U.S. dollars.
One common means of hedging against risk is the purchase of insurance to protect against financial loss due to accidental property damage or loss, personal injury, or loss of life.
Categories of hedgeable risk
There are varying types of risk that can be protected against with a hedge. Those types of risks include:
Commodity risk : the risk that arises from potential movements in the value of commodity contracts, which include agricultural products, metals, and energy products.[2]
Credit risk : the risk that money owing will not be paid by an obligor. Since credit risk is the natural business of banks, but an unwanted risk for commercial traders, an early market developed between banks and traders that involved selling obligations at a discounted rate.
Currency risk (also known as Foreign Exchange Risk hedging) is used both by financial investors to deflect the risks they encounter when investing abroad and by non-financial actors in the global economy for whom multi-currency activities are a necessary evil rather than a desired state of exposure.
Interest rate risk : the risk that the relative value of an interest-bearing liability, such as a loan or a bond, will worsen due to an interest rate increase. Interest rate risks can be hedged using fixed-income instruments or interest rate swaps.
Equity risk : the risk that one's investments will depreciate because of stock market dynamics causing one to lose money.
Volatility risk : is the threat that an exchange rate movement poses to an investor's portfolio in a foreign currency.
Volumetric risk : the risk that a customer demands more or less of a product than expected.
Hedging equity and equity futures
Equity in a portfolio can be hedged by taking an opposite position in futures. To protect your stock picking against systematic market risk, futures are shorted when equity is purchased, or long futures when stock is shorted.
One way to hedge is the market neutral approach. In this approach, an equivalent dollar amount in the stock trade is taken in futures – for example, by buying 10,000 GBP worth of Vodafone and shorting 10,000 worth of FTSE futures.
Another way to hedge is the beta neutral. Beta is the historical correlation between a stock and an index. If the beta of a Vodafone stock is 2, then for a 10,000 GBP long position in Vodafone an investor would hedge with a 20,000 GBP equivalent short position in the FTSE futures (the index in which Vodafone trades).
Futures contracts and forward contracts are means of hedging against the risk of adverse market movements. These originally developed out of commodity markets in the 19th century, but over the last fifty years a large global market developed in products to hedge financial market risk.
Futures hedging
Investors who primarily trade in futures may hedge their futures against synthetic futures. A synthetic in this case is a synthetic future comprising a call and a put position. Long synthetic futures means long call and short put at the same expiry price. To hedge against a long futures trade a short position in synthetics can be established, and vice versa.
Stack hedging is a strategy which involves buying various futures contracts that are concentrated in nearby delivery months to increase the liquidity position. It is generally used by investors to ensure the surety of their earnings for a longer period of time.
Contract for difference
A contract for difference (CFD) is a two-way hedge or swap contract that allows the seller and purchaser to fix the price of a volatile commodity. Consider a deal between an electricity producer
and an electricity retailer, both of whom trade through an electricity market pool. If the producer and the retailer agree to a strike price of $50 per MWh, for 1 MWh in a trading period, and if the actual pool price is $70, then the producer gets $70 from the pool but has to rebate $20 (the "difference" between the strike price and the pool price) to the retailer. Conversely, the retailer pays the difference to the producer if the pool price is lower than the agreed upon contractual strike price. In effect, the pool volatility is nullified and the parties pay and receive $50 per MWh. However, the party who pays the difference is "out of the money" because without the hedge they would have received the benefit of the pool price.
STOCK INDEX FUTURES: HEDGING OR SPECULATIVE MARKETS?The market structure of futures contacts is a neglected topic which has implications for futures pricing, regulation, and contract success. This paper examines the hedging versus speculative market structure for stock index futures contracts. Open interest data for speculators, hedgers, and non-reporting traders are analyzed across contracts and across time in order to determine the relationship between these categories and total open interest. Various measures of speculative and hedging importance show that most of the stock index futures contracts have matured from speculative markets to hedging markets over time. The S&P 500 contract is most closely associated with hedging, while speculation has almost no effect on this contract's total open interest. Other stock index futures have a greater speculative component, especially the NYSEcontract.STOCK INDEX FUTURES: HEDGING OR SPECULATIVE MARKETS?I. INTRODUCTIONThe relative importance of hedging versus speculation for stock index futures has been a vigorously debated topic since the futures exchanges proposed contracts in this area. While cash settlement of these contracts created controversy and legal issues associated with gambling, the key issue was the potential for excessive and unwarranted speculation. These fears concerning speculation caused the CFTC and the exchanges to require large initial margins for speculative positions, as well as to delay the implementation of these contracts for several years. The two criteria for CFTC approval of a futures contract are price discovery and hedging ability. In fact, the existence of futures markets are often linked to the success of such markets to transfer risk from hedgers to speculators. While studies by Peck (1980a,b) provide evidence that large agricultural markets became less speculative and more of a hedging market from the 1960s to the 1970s, comparable evidence does not exist for stock index futures.This paper examines the structure of the stock index futures market by analyzing the relative importance of large speculators, large hedgers, and non-reporting users of stock index futures. These categories are compared and analyzed across contracts and across time. The purpose of this paper is to determine the relative importance of these categories and to provide evidence that stock index futures have developed from speculative markets to hedging markets.II. THE ISSUES AND THE DATAA.
Market Structure in Stock Index Futures Markets: The Issues Determining the market structure of futures markets shows whether a particular futures contract is a hedging or a speculative contract, and whether the futures are dominated by large or small traders. Inparticular, stock index futures have been the brunt of numerous allegations that speculation has an undue influence on these futures and that the financial markets would be better served without these "dens of inequity". However, if these markets are truly hedging markets then they provide an important service to the financial community that can not be adequately obtained elsewhere.Market structure for stock index futures is examined in this paper by analyzing the total open interest for the large noncommercial, large commercial, large spreading, and the non-reporting categories of the CFTC's Commitments to Traders. The noncommercial category is the speculative accounts, while the commercial category is the hedging accounts.
The data is also divided into long and short positions. The structure of these markets is investigated by calculating the relative proportions of these categories, both over time and across contracts, and by determining various measures of the speculative and hedging activity in these markets. Such measures include the net hedging balance, the speculative and hedging ratios, the speculative index, and the R values from regressions of changes in the hedging/speculative open interest to changes in the total open interest.The proportions of the four categories across contracts and time provide an initial measure of the relative importance of the speculative, hedging, and non-reporting categories. Determining the net hedging balance, speculative and hedging ratios, and speculation index provide morespecific evidence on the speculative versus hedging aspects of the stock index futures markets.Net hedging balance between short and long hedgers is deemed important for long-term stability in the market. Hence, a market where speculators provide a temporal bridge between temporary long and short imbalances is deemed necessary, but a market where speculators are needed to offset a large consistent imbalance between long and short hedging positions creates potential for an unstable market. Hence, whether and when hedging balance occurs is an important issue for market stability and maturity.The speculative and hedging ratios and the speculative index provide alternative measures of the balance in the market, with the objective of determining the extent of the excess speculation in the market in relation to the amount of hedging.
The speculative ratio is defined as:SR = SL/HS if HS>HL or = SS/HL if HL>HS
The hedging ratio is determined by:HR = HL/HS if HS>HL or = HS/HL if HL>HSWhere:SR = the speculative ratio, HR = the hedging ratio, SL = the amount of long speculationSS = the amount of short speculation, HL = the amount of long hedging, HS = the amount of short hedging.
The speculative and hedging ratios are used separately and in conjunction with one another to determine how the larger component of the long/short hedging category is offset. For example, when short hedging is larger than long hedging then the speculative ratio examines the ratio of long speculation to short hedging, while the hedging ratio examines the ratio of long hedging to short hedging.When short and long hedging are not balanced then speculation must create the needed balance. Hence, when HS>HL then long speculation creates the net balance, with such speculation occurring either in the noncommercial or the non-reporting categories. To the extent that excess long speculation exists then additional (short) speculation must come into the market to create an overall balance between the long and short open interest figures. Determining the speculative ratio examines the relationship between the dominant speculative and hedging long/short categories. Meanwhile, the hedging ratio measures the extent of the balance between the short and long hedging open interest. The relationship between the two ratios provides evidence concerning whether speculation, hedging, or neither dominate a particular market. The speculative index provides an alternative measure of the relationship between speculation and hedging. The speculative index, as first stated by Working (1960), is defined as:
SI = 1 + SS/(HL + HS) if HS>HLor = 1 + SL/(HS + HL) if HL>HS
Where:SI = the speculative index.The speculative index concentrates on the proportion of speculation that exists that is not needed to balance net hedging. Thus, when short hedging dominates then short speculation is not needed to make the market function or to create a net hedging balance. Hence, such short speculationnecessitates additional long speculation to balance the market. The speculative index provides a measure of the amount of excess speculation in percentage terms. Large values indicate a speculative market and small values a balanced market.
Finally, another method to examine the relationship between total open interest and the categories of hedging and speculation is to calculate regression results between the changes in total open interest and the changes in the individual categories. The slopes of the regressionequations provide the average relationships between the categories and total open interest changes, while the R values show the percentage of the changes in total open interest explained by the changes in the hedging/speculative component of open interest. The category with thelarger R value is the one with a closer association between that categoryand the changes in total open interest.B. The Data
The CFTC Commitments to Traders (1983-1988) is employed to obtain month end open interest totals for noncommercial (speculators), commercials(hedgers), spreaders, and non-reporting traders.Each category isreported both in terms of long and short positions at the end of eachmonth. This study separates the data into the March quarterly cycle and the February quarterly cycle. The March cycle encompasses the March, June, September, and December open interest data. The February cycle considers the February, May, August, and November data. The data is examined across contracts and across time. The stock index futures contracts analyzed in this study are the S&P500, NYSE, MMI Maxi, Value Line, S&P100, and MMI Mini contacts. Since both the long and the short open interest categories equal the total open interest,the proportions calculated in this study add to 200%.III. EXAMINING THE OPEN INTEREST BY CATEGORYThe initial measure of the relationship between noncommercial, commercial, and non-reporting open interest is to obtain their relative proportions of the total open interest. Table 1 determines these proportions in terms of the sum of the long and short positions for each stock index futures, for each year they were traded, and for the March and February cycles.
Hedging with stock index futures
An investor with a large portfolio of stocks may want to hedge against a stock market decline by using futures contracts. A hedge is purchasing a derivative security that will generate profits to offset any losses in the portfolio and still allow the portfolio to accumulate gains if the market goes up in value. Futures are popular for hedging because of the liquidity of futures contracts and the different stock market indexes that are represented by futures contracts.
hedging contracts
nstructions
Determine which stock market index best reflects the composition of your stock portfolio. The Dow Jones Industrial Average is an index of large, blue chip stocks. The S&P 500 is a broad market index. The NASDAQ 100 index is primarily large tech stocks. Pick the index that is the closest match to your portfolio.
Determine whether you will hedge with the standard or"e-mini" futures contracts. The standard contracts will hedge a larger amount of stock with a single contract. The standard contracts will provide hedging for $250,000 to $300,000 per contract. E-mini contracts have a stock value of $40,000 to $60,000.
Calculate how many futures contracts you will need to hedge your stock portfolio. The value of a futures contract is the futures price times a multiplier. The futures price will be very close to the stock index of the specific futures contract. Multipliers for the futures listed above are for the DJIA: 5, 10 or 25. For the standard S&P500 and NASDAQ 100: 250 and 100, respectively. E-mini S&P and NASDAQ 100 multipliers are 40 and 20. For example, the NASDAQ 100 has a value of 1,980, so the e-mini contract covers $39,600
worth of stock. You have a $200,000 tech stock portfolio, so you would need five e-mini NASDAQ 100 futures contracts to hedge your portfolio.
Sell the futures contracts short. Futures sold short will increase in value as the stock index declines. Futures contracts require a margin deposit for the contracts traded. The deposit requirement is set by the futures exchange and is 7 to 10 percent of the contract value for stock index futures. The e-mini NASDAQ 100 futures have a margin requirement of $3,500 per contract.
Monitor the price of the futures contracts and the tracked stock index. As the index declines, the value of the futures position will increase to offset the losses in your stock portfolio. If the stock index goes up in value, be ready to close out the futures positions to avoid a large loss on the
Futures trading in BSE and NSE:
We must try to understand the meaning of the word derivative actually. Derivatives are basically those financial instruments which aim to derive their value from some other asset called the underlying asset and have a monetary value as well. Now the underlying asset can be anything actually. It can be currency; it may be gold, stock or any other commodity.
So briefly we can say that derivative is not an asset but it can be defined as an agreement or contract deal of transferring the real asset in future whenever it is exercised. In the contract the price amount and the date of execution is mentioned according to the agreement of the parties. The varieties of derivatives that are usually found are options, future and swap. The options and futures are ones which are found to be common.
But you really need to understand a few components for the better understanding of derivatives.
Holder: this person can be defined as the buyer of the agreement. By doing so he can actually agree to sell or buy the underlying asset.
Seller: he is the person who would sell the contract to holder.
Expiry date: this is the date on which the agreement would mature or be exercised.
Strike price: this is the price at which the derivative can be exercised and it would be decided right at the moment of entering into agreement.
Premium: this is the price paid by the buyer for buying an option contract. This premium is not expected to be paid for future contract.
The reason why people find this contract so interesting and good is mainly because it is not an asset itself, so it is different from many other financial instruments. It is an agreement where transfer of real or actual assets can be possible in future trading in India. But the next valid question is why should one enter such an agreement of doing transactions in future? Why should
not a person directly buy the real assets at current value from the spot market? Why should any one go for an agreement to pull the contract in the future?
The answer to all these questions is one, and that is protection. Derivatives are treated as instruments of protection against any unpredictable fall or rise in price of the underlying assets.
The second reason is that derivatives are in a position to promise better returns with a low capital investment as collated to the amount that will be invested when buying shares directly from the spot market.
Now let us have a look at the types of derivatives.
Forward contract: they cannot be traded in exchange and their date in future and the price are decided during the time of negotiation. It is decided between the contracting parties actually.
Future contracts: the price and date of this kind of a financial instrument is decided during the negotiation period between the dealing parties and they can be traded on the stock exchange actually.
Option contract: it is a little different since it gives the holder the right to it but presents no obligation of exercising the right. Call option presents the right to buy while put option presents the right to sell. And these are done at the strike price on pre determined date.
Warrants: these can extend for a period of 3 to 7 years at least and hence can be defined as long term. They are issued for the purpose of raising finance without dividends or interests. This kind of security is issued by corporation with a bond or preferred stock.
Swap contracts: it is an agreement to exchange a set of financial obligations for another according to the terms of agreement.
Swap Options: they are options on swaps. They give the right to enter into call as well as put options.
Fd remaining chapters:
an option is a derivative financial instrument that establishes a contract between two parties concerning the buying or selling of an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in some specific transaction on the asset, while the seller incurs the obligation to fulfill the transaction if so requested by the buyer. The price of an option derives from the difference between the reference price and the value of the underlying asset (commonly a stock, a bond, a currency or a futures contract) plus a premium based on the time remaining until the expiration of the option. Other types of options exist, and options can in principle be created for any type of valuable asset.
An option which conveys the right to buy something is called a call; an option which conveys the right to sell is called a put. The reference price at which the underlying may be traded is called the strike price or exercise price. The process of activating an option and thereby trading the underlying at the agreed-upon price is referred to as exercising it. Most options have an expiration date. If the option is not exercised by the expiration date, it becomes void and worthless.
In return for granting the option, called writing the option, the originator of the option collects a payment, the premium, from the buyer. The writer of an option must make good on delivering (or receiving) the underlying asset or its cash equivalent, if the option is exercised.
An option can usually be sold by its original buyer to another party. Many options are created in standardized form and traded on an anonymous options exchange among the general public, while other over-the-counter options are customized ad hoc to the desires of the buyer, usually by an investment bank.[1][2]
The Role of an Option Market
These exchanges ensure that the contract terms are backed by the credit of the exchange. They also safeguard the anonymity of the counterparties and enforce market regulations to ensure that the trades remain fair and transparent. During fast trading conditions, these exchanges ensure the maintenance of orderly markets.
here are two types of options; namely:
Call options Put options
We shall discuss both these types of options. You are advised to follow the thought, to understand the concept. The names and the prices in the illustrations below are not in real time and have only been used to help explain these options.
Call Options: The call options give the taker (or buyer) the right, but not the obligation, to buy the underlying stocks (or shares) at a predetermined price, on or before a determined date.
Illustration 1: Let's say Raj purchases 1 Satyam Computer (SATCOM) AUG 150 Call at a Premium of 8.
This contract allows Raj to buy 100 shares of SATCOM at INR 150.00 per share at any time between the current date and the end of August. For this privilege, Raj pays a fee of INR 800.00; that is INR 8.00 a share for 100 shares.
The buyer of a "call" has purchased the right to buy and for that he pays a premium.
Now, let us see how one can profit from buying an option.
Raj purchases a December Call option at INR 40.00 for a premium of INR 15.00. That is he has purchased the right to buy that underlying share for INR 40.00 by the end of December. If the price of the underlying stock rises above INR 55.00 (that is INR 40.00 + INR 15.00) he will break even and start making a profit. However, to book this profit he would have to exercise this option on or before the expiry date. Now, suppose the price of the underlying stock does not rise but falls. Then Raj would choose not to exercise the option and forgo the premium of INR 15.00 and thus limit his loss to this amount only.
If the Premium = INR 15.00 and the Strike price of the Call Option = INR 40.00, then the Break even point = INR 15.00 + INR 40.00 = INR 55.00. That is to say that the price of the underlying stock would have to rise to INR 55.00 before Raj would break even in his transaction.
Let us take another example of a Call Option on the Nifty to understand the concept better.
Let's say Nifty is at 1310. The following Nifty Options are trading at the following quotes:
OPTIONS CONTRACT STRIKE PRICE CALL PREMIUMDecember Nifty 1325 INR 6,000.00 1345 INR 2,000.00January Nifty 1325 INR 4,500.00 1345 INR 5,000.00
A trader is of the view that the index or Nifty would go up to 1400 in January, but does not want the risk of prices going down. Therefore, he buys 10 Options of January contracts at 1345. He pays a premium for buying these Call Options (that is the right to buy these contract) for INR 500.00 X 10 = INR 5,000.00.
In January, the Nifty index goes up to 1365. He sells the Call Options or exercises the option and takes the difference between the Nifty Spot and the Strike price of his Call Option contracts (that is INR 1365.00 - INR 1345 = INR 20.00). Now the market lot of the Nifty contract is 200. So, the trader books a profit of INR 20.00 X 200 = INR 4,000.00 per contract. Now, as he had bought 10 Call Options contracts his total profit would be INR 4,000.00 X 10 = INR 40,000.00.
He had paid INR 5,000.00 towards the premium for buying these Call Options. So he would have earned INR 40,000.00 less INR 5,000.00 which is INR 35,000.00 when he exercised these Call Option contracts.
If, on the other had the Nifty had fallen below 1345, then the trader will not exercise his right and would opt to forego the premium of INR 5,000.00 he had paid initially. So, in
case the Nifty falls further below the 1345 level the traders loss is limited to the premium he paid upfront, but the profit potential is unlimited.
Call Options: Long and Short Positions:
When you expect prices to rise, then you take a long position by buying the Call Option. You are bullish on the underlying security.
When you expect prices to fall, then you take a short position by selling the Call Option. You are bearish on the underlying security.
Put Options: A Put Option gives the holder the right to sell a specified number of shares of an underlying security at a fixed price for a period of time.
Let's say Raj purchases 1 Infosys Technology Aug 3500 Put - Premium 200.
This contract allows Raj to sell 100 shares of Infosys Technology at INR 3,500.00 per share at any time between the current date and the end of August. To have this privilege, Raj pays a premium of INR 20,000.00 (that is INR 200.00 per share for 100 shares). The buyer of a put has purchased a right to sell.
To explain this further, let's say Raj is of the view that a stock is overpriced and its price would fall in the future, but he does not want to take the risk in the event of the price rising. So, he purchases a Put option at INR 70.00 on Stock 'X'. By purchasing the put option Raj has the right to sell the stock at INR 70.00, but he has to pay a premium of INR 15.00 for this contract.
So Raj would breakeven only after the stock falls below INR 55.00 (that is INR 70.00 less INR 15.00) and would start making a profit on this contract when the stock price falls below INR 55.00.
Let us illustrate this further. A trader on 15 December is of the view that Wipro is overpriced and would fall in the future, but does not want to take the risk in the event the price rises. So, he purchases a Put option on Wipro. The quotes are as under:
Spot INR 1,040.00 Jan Put 1050 INR 10.00
Jan Put 1070 INR 30.00
The trader purchases 1000 Wipro Put at Strike price 1070 at Put price of INR 30.00. He pays a Put premium of INR 30,000.00. His position in the following price points situations is discussed below:
1. Jan Spot price of Wipro = 10202. Jan Spot price of Wipro = 1080
In the first situation, the trader has the right to sell 1000 Wipro shares at INR 1,070.00 , the Spot price of which is INR 1,020.00. By exercising the Put option he earns INR (1070 - 1020) = INR 50.00 per put, which totals INR 50,000.00. His net income is INR 50,000.00 less INR 30,000.00 (that is the premium paid upfront) = INR 20,000.00.
In the second price situation, the price is higher in the Spot market, so the trader would not sell at a lower price. In this case he would have to let his Put option expire unexercised. His loss here would be initial premium paid for the Put option contracts, that is INR 30,000.00.
Put Options: Long and Short Positions:
When you expect price to fall, then you take a long position by buying Puts. You are bearish.
When you expect prices to rise, then you take a short position by selling Puts. You are bullish.
Call Options and Put Options: Long and Short Positions:
CALL OPTIONS PUT OPTIONSIf you expect a fall in price (Bearish)
Short Long
If you expect a rise in price (Bullish)
Long Short
We have provided a matrix below to summarize the above discussion on Call and Put options:
CALL OPTION BUYER CALL OPTION WRITER (SELLER)Pays the premium Receives the premiumHas right to exercise and buy the underlying shares
Obligation to sell shares, if contract is exercised
Profits from rising prices Profits from falling prices or remains neutralLimited loss, potentially unlimited gain Potentially unlimited loss, limited gainPUT OPTION BUYER PUT OPTION WRITER (SELLER)Pays the premium Receives the premiumHas right to exercise and sell the underlying shares
Obligation to buy the shares if contract is exercised
Profits from falling prices Profits from rising prices or remains neutralLimited loss, potentially unlimited gain Potentially unlimited loss, limited gain
Types
The Options can be classified into following types:
[edit] Exchange-traded options
Exchange-traded options (also called "listed options") are a class of exchange-traded derivatives. Exchange traded options have standardized contracts, and are settled through a clearing house with fulfillment guaranteed by the credit of the exchange. Since the contracts are standardized, accurate pricing models are often available. Exchange-traded options include:[4][5]
o stock options,
o commodity options ,
o bond options and other interest rate options
o stock market index options or, simply, index options and
o options on futures contracts
o callable bull/bear contract
[edit] Over-the-counter
Over-the-counter options (OTC options, also called "dealer options") are traded between two private parties, and are not listed on an exchange. The terms of an OTC option are unrestricted and may be individually tailored to meet any business need. In general, at least one of the counterparties to an OTC option is a well-capitalized institution. Option types commonly traded over the counter include:
1. interest rate options
2. currency cross rate options, and
3. options on swaps or swaptions.
[edit] Other option types
Another important class of options, particularly in the U.S., are employee stock options, which are awarded by a company to their employees as a form of incentive compensation. Other types of options exist in many financial contracts, for example real estate options are often used to assemble large parcels of land, and prepayment options are usually included in mortgage loans. However, many of the valuation and risk management principles apply across all financial options.
[edit] Option styles
Main article: Option style
Naming conventions are used to help identify properties common to many different types of options. These include:
European option - an option that may only be exercised on expiration. American option - an option that may be exercised on any trading day on or
before expiry.
Bermudan option - an option that may be exercised only on specified dates on or before expiration.
Barrier option - any option with the general characteristic that the underlying security's price must pass a certain level or "barrier" before it can be exercised.
Exotic option - any of a broad category of options that may include complex financial structures.[6]
Vanilla option - any option that is not exotic.
[edit] Valuation models
Main article: Valuation of options
The value of an option can be estimated using a variety of quantitative techniques based on the concept of risk neutral pricing and using stochastic calculus. The most basic model is the Black-Scholes model. More sophisticated models are used to model the volatility smile. These models are implemented using a variety of numerical techniques.[7] In general, standard option valuation models depend on the following factors:
The current market price of the underlying security, the strike price of the option, particularly in relation to the current market price of
the underlier (in the money vs. out of the money),
the cost of holding a position in the underlying security, including interest and dividends,
the time to expiration together with any restrictions on when exercise may occur, and
an estimate of the future volatility of the underlying security's price over the life of the option.
More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates.
The following are some of the principal valuation techniques used in practice to evaluate option contracts.
[edit] Black-Scholes
Main article: Black–Scholes
Following early work by Louis Bachelier and later work by Edward O. Thorp, Fischer Black and Myron Scholes made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative dependent on a non-dividend-paying stock. By employing the technique of constructing a risk neutral portfolio that replicates the returns of holding an option, Black and Scholes produced a closed-form solution for a European option's theoretical price.[8] At the same time, the model generates hedge parameters necessary for effective risk management of option holdings. While the ideas behind the Black-Scholes model were ground-breaking and eventually led to Scholes and Merton receiving the Swedish Central Bank's associated Prize for Achievement in Economics (a.k.a., the Nobel Prize in Economics),[9] the application of the model in actual options trading is clumsy because of the assumptions of continuous (or no) dividend payment, constant volatility, and a constant interest rate. Nevertheless, the Black-Scholes model is still one of the most important methods and foundations for the existing financial market in which the result is within the reasonable range.[10]
[edit] Stochastic volatility models
Main article: Heston model
Since the market crash of 1987, it has been observed that market implied volatility for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility is stochastic, varying both for time and for the price level of the underlying security. Stochastic volatility models have been developed including one developed by S.L. Heston.[11] One principal advantage of the Heston model is that it can be solved in closed-form, while other stochastic volatility models require complex numerical methods.[11]
See also: SABR Volatility Model
[edit] Model implementation
Further information: Valuation of options
Once a valuation model has been chosen, there are a number of different techniques used to take the mathematical models to implement the models.
[edit] Analytic techniques
In some cases, one can take the mathematical model and using analytical methods develop closed form solutions such as Black-Scholes and the Black model. The resulting solutions are readily computable, as are their "Greeks".
[edit] Binomial tree pricing model
Main article: Binomial options pricing model
Closely following the derivation of Black and Scholes, John Cox, Stephen Ross and Mark Rubinstein developed the original version of the binomial options pricing model.[12] [13] It models the dynamics of the option's theoretical value for discrete time intervals over the option's life. The model starts with a binomial tree of discrete future possible underlying stock prices. By constructing a riskless portfolio of an option and stock (as in the Black-Scholes model) a simple formula can be used to find the option price at each node in the tree. This value can approximate the theoretical value produced by Black Scholes, to the desired degree of precision. However, the binomial model is considered more accurate than Black-Scholes because it is more flexible; e.g., discrete future dividend payments can be modeled correctly at the proper forward time steps, and American options can be modeled as well as European ones. Binomial models are widely used by professional option traders. The Trinomial tree is a similar model, allowing for an up, down or stable path; although considered more accurate, particularly when fewer time-steps are modelled, it is less commonly used as its implementation is more complex.
[edit] Monte Carlo models
Main article: Monte Carlo methods for option pricing
For many classes of options, traditional valuation techniques are intractable because of the complexity of the instrument. In these cases, a Monte Carlo approach may often be useful. Rather than attempt to solve the differential equations of motion that describe the option's value in relation to the underlying security's price, a Monte Carlo model uses simulation to generate random price paths of the underlying asset, each of which results in a payoff for the option. The average of these payoffs can be discounted to yield an expectation value for the option.[14] Note though, that despite its flexibility, using simulation for American styled options is somewhat more complex than for lattice based models.
[edit] Finite difference models
Main article: Finite difference methods for option pricing
The equations used to model the option are often expressed as partial differential equations (see for example Black–Scholes PDE). Once expressed in this form, a finite difference model can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including: explicit finite difference, implicit finite difference and the Crank-Nicholson method. A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method. Although the Finite difference approach is mathematically sophisticated, it is particularly useful where changes are assumed over time in model inputs - for example dividend yield, risk free rate, or volatility, or some combination of these - that are not tractable in closed form.
[edit] Other models
Other numerical implementations which have been used to value options include finite element methods. Additionally, various short rate models have been developed for the valuation of interest rate derivatives, bond options and swaptions. These, similarly, allow for closed-form, lattice-based, and simulation-based modelling, with corresponding advantages and considerations.
[edit] Risks
As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, the return from holding an option varies non-linearly with the value of the underlier and other factors. Therefore, the risks associated with holding options are more complicated to understand and predict.
In general, the change in the value of an option can be derived from Ito's lemma as:
where the Greeks Δ, Γ, κ and θ are the standard hedge parameters calculated from an option valuation model, such as Black-Scholes, and dS, dσ and dt are unit changes in the underlier price, the underlier volatility and time, respectively.
Thus, at any point in time, one can estimate the risk inherent in holding an option by calculating its hedge parameters and then estimating the expected change in the model inputs, dS, dσ and dt, provided the changes in these values are small. This technique can be used effectively to understand and manage the risks associated with standard options. For instance, by offsetting a holding in an option with the quantity − Δ of shares in the underlier, a trader can form a delta neutral portfolio that is hedged from loss for small changes in the underlier price. The corresponding price sensitivity formula for this portfolio Π is:
[edit] Example
A call option expiring in 99 days on 100 shares of XYZ stock is struck at $50, with XYZ currently trading at $48. With future realized volatility over the life of the option estimated at 25%, the theoretical value of the option is $1.89. The hedge parameters Δ, Γ, κ, θ are (0.439, 0.0631, 9.6, and -0.022), respectively. Assume that on the following day, XYZ stock rises to $48.5 and volatility falls to 23.5%. We can calculate the estimated value of the call option by applying the hedge parameters to the new model inputs as:
Under this scenario, the value of the option increases by $0.0614 to $1.9514, realizing a profit of $6.14. Note that for a delta neutral portfolio, where by the trader had also sold 44 shares of XYZ stock as a hedge, the net loss under the same scenario would be ($15.86).
[edit] Pin risk
Main article: Pin risk
A special situation called pin risk can arise when the underlier closes at or very close to the option's strike value on the last day the option is traded prior to expiration. The option writer (seller) may not know with certainty whether or not the option will actually be exercised or be allowed to expire worthless. Therefore, the option writer may end up with a large, unwanted residual position in the underlier when the markets open on the next trading day after expiration, regardless of their best efforts to avoid such a residual.
[edit] Counterparty risk
A further, often ignored, risk in derivatives such as options is counterparty risk. In an option contract this risk is that the seller won't sell or buy the underlying asset as agreed. The risk can be minimized by using a financially strong intermediary able to make good on the trade, but in a major panic or crash the number of defaults can overwhelm even the strongest intermediaries.
[edit] Trading
The most common way to trade options is via standardized options contracts that are listed by various futures and options exchanges. [15] Listings and prices are tracked and can be looked up by ticker symbol. By publishing continuous, live markets for option prices, an exchange enables independent parties to engage in price discovery and execute transactions. As an intermediary to both sides of the transaction, the benefits the exchange provides to the transaction include:
fulfillment of the contract is backed by the credit of the exchange, which typically has the highest rating (AAA),
counterparties remain anonymous,
enforcement of market regulation to ensure fairness and transparency, and
maintenance of orderly markets, especially during fast trading conditions.
Over-the-counter options contracts are not traded on exchanges, but instead between two independent parties. Ordinarily, at least one of the counterparties is a well-
capitalized institution. By avoiding an exchange, users of OTC options can narrowly tailor the terms of the option contract to suit individual business requirements. In addition, OTC option transactions generally do not need to be advertised to the market and face little or no regulatory requirements. However, OTC counterparties must establish credit lines with each other, and conform to each others clearing and settlement procedures.
With few exceptions,[16] there are no secondary markets for employee stock options. These must either be exercised by the original grantee or allowed to expire worthless.
The basic trades of traded stock options (American style)
These trades are described from the point of view of a speculator. If they are combined with other positions, they can also be used in hedging. An option contract in US markets usually represents 100 shares of the underlying security.[17]
[edit] Long call
Payoff from buying a call.
A trader who believes that a stock's price will increase might buy the right to purchase the stock (a call option) rather than just purchase the stock itself. He would have no obligation to buy the stock, only the right to do so until the expiration date. If the stock price at expiration is above the exercise price by more than the premium (price) paid, he will profit. If the stock price at expiration is lower than the exercise price, he will let the call contract expire worthless, and only lose the amount of the premium. A trader might buy the option instead of shares, because for the same amount of money, he can control (leverage) a much larger number of shares.
[edit] Long put
Payoff from buying a put.
A trader who believes that a stock's price will decrease can buy the right to sell the stock at a fixed price (a put option). He will be under no obligation to sell the stock, but has the right to do so until the expiration date. If the stock price at expiration is below the exercise price by more than the premium paid, he will profit. If the stock price at expiration is above the exercise price, he will let the put contract expire worthless and only lose the premium paid.
[edit] Short call
Payoff from writing a call.
A trader who believes that a stock price will decrease, can sell the stock short or instead sell, or "write," a call. The trader selling a call has an obligation to sell the stock to the call buyer at the buyer's option. If the stock price decreases, the short call position will make a profit in the amount of the premium. If the stock price increases over the exercise price by more than the amount of the premium, the short will lose money, with the potential loss unlimited.
[edit] Short put
Payoff from writing a put.
A trader who believes that a stock price will increase can buy the stock or instead sell, or "write", a put. The trader selling a put has an obligation to buy the stock from the put buyer at the put buyer's option. If the stock price at expiration is above the exercise price, the short put position will make a profit in the amount of the premium. If the stock price at expiration is below the exercise price by more than the amount of the premium, the trader will lose money, with the potential loss being up to the full value of the stock. A benchmark index for the performance of a cash-secured short put option position is the CBOE S&P 500 PutWrite Index (ticker PUT).
[edit] Option strategies
Main article: Option strategies
Payoffs from buying a butterfly spread.
Payoffs from selling a straddle.
Payoffs from a covered call.
Combining any of the four basic kinds of option trades (possibly with different exercise prices and maturities) and the two basic kinds of stock trades (long and short) allows a variety of options strategies. Simple strategies usually combine only a few trades, while more complicated strategies can combine several.
Strategies are often used to engineer a particular risk profile to movements in the underlying security. For example, buying a butterfly spread (long one X1 call, short two X2 calls, and long one X3 call) allows a trader to profit if the stock price on the expiration date is near the middle exercise price, X2, and does not expose the trader to a large loss.
An Iron condor is a strategy that is similar to a butterfly spread, but with different strikes for the short options - offering a larger likelihood of profit but with a lower net credit compared to the butterfly spread.
Selling a straddle (selling both a put and a call at the same exercise price) would give a trader a greater profit than a butterfly if the final stock price is near the exercise price, but might result in a large loss.
Similar to the straddle is the strangle which is also constructed by a call and a put, but whose strikes are different, reducing the net debit of the trade, but also reducing the likelihood of profit in the trade.
One well-known strategy is the covered call, in which a trader buys a stock (or holds a previously-purchased long stock position), and sells a call. If the stock price rises above the exercise price, the call will be exercised and the trader will get a fixed profit. If the stock price falls, the call will not be exercised, and any loss incurred to the trader will be partially offset by the premium received from selling the call. Overall, the payoffs match the payoffs from selling a put. This relationship is known as put-call parity and offers insights for financial theory. A benchmark index for the performance of a buy-write strategy is the CBOE S&P 500 BuyWrite Index (ticker symbol BXM).
[edit] Historical uses of options
Contracts similar to options are believed to have been used since ancient times. In the real estate market, call options have long been used to assemble large parcels of land from separate owners; e.g., a developer pays for the right to buy several adjacent plots, but is not obligated to buy these plots and might not unless he can buy all the plots in the entire parcel. Film or theatrical producers often buy the right — but not the obligation — to dramatize a specific book or script. Lines of credit give the potential borrower the right — but not the obligation — to borrow within a specified time period.
Many choices, or embedded options, have traditionally been included in bond contracts. For example many bonds are convertible into common stock at the buyer's option, or may be called (bought back) at specified prices at the issuer's option. Mortgage borrowers have long had the option to repay the loan early, which corresponds to a callable bond option.
In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign of William and Mary.[18]
Privileges were options sold over the counter in nineteenth century America, with both puts and calls on shares offered by specialized dealers. Their exercise price was fixed at a rounded-off market price on the day or week that the option was bought, and the expiry date was generally three months after purchase. They were not traded in secondary markets.
Supposedly the first option buyer in the world was the ancient Greek mathematician and philosopher Thales of Miletus. On a certain occasion, it was predicted that the season's olive harvest would be larger than usual, and during the off-season he acquired the right to use a number of olive presses the following spring. When spring came and the olive
harvest was larger than expected he exercised his options and then rented the presses out at much higher price than he paid for his 'option'.
Types of option contract.In forex as in the stock market there are several types of options. In most categories, there are two forms of options: call and put options. In their regular and most simple configuration, these belong to the "vanilla” category. At Finotec, we have added for your convenience two types of options strategies in this category:the strangle and the straddle options strategies. These combine both forms of options (call & put) in different ways and can be assimilated to basic option strategies.On the Finotec Trading Platform, you can also trade other forex options types such as "barrier” and "binary” (also known as "digital” options). They both belong to the wider category of "exotic options,” which are very developed in the foreign exchange market, and which refer either to variations on the payout characteristics of plain vanilla options or to options whose validation or invalidation is conditioned by additional factors (other than just the expiration time and the strike rate).Vanilla Options
Call PutStrangle StrategyStraddle Strategy
Exotic Options Barrier Binary Knock in One touch Knock out No touch
Reverse knock in Double one touch
Reverse knock out Double no touch
Vanilla Forex Options:Plain vanilla options refer to standard forex options types: they are defined by a standard strike price and expiration date and refer to the buying or selling of a standard call or put option. They give the buyer (holder) the right, but not the obligation, to buy or sell a set amount of currency at a certain rate and before a certain date. For this right, the holder of the options contract pays the premium (option price) to the seller (writer). According to evolution of the market and the profitability of the option, the holder of the option contract will decide to exercise or not his option. On the Finotec Trading Platform, traders may buy or sell call and put options. Note that put and call options are
two separate contracts different from one another and not the other side of the same transaction.
Call option :A forex call option gives the buyer the right, but not the obligation, to buy a predetermined amount of currency from the options contract seller at a set rate (the "strike price”) and before a specific date (the expiration date). In the case of a regular call option, the buyer believes that the rate will go up and will want to buy it at lower price. For that right, the buyer will pay the premium.
Put option: A forex put option gives the buyer the right, but not the obligation to sell a predetermined amount of currency at a set price (strike price) and within a specific time (before or on the expiration date). The buyer believes that the rate will drop below the strike price before the expiration date so he’ll want to sell it at a higher and not lower rate. In return for this right, the buyer pays the premium to the writer.
Option Strategies: Traders make their own option strategies by combining different options. With Finotec, two option strategies are directly available from our platform: the strangle option strategy, and the straddle option strategy. Both these strategies are a combination of two vanilla options. This means that you don’t have to open two options separately to implement either of those strategies, you just click “strangle” or “straddle” and fill in the requested inputs and both options will open automatically at the same time.
Strangle Strategy: This options strategy consists in buying or selling a call and a put option at different strike prices. A trader will get a long strangle option (buy) in expectation of a sharp swing of the exchange rate in either direction. The long strangle strategy has unlimited profit potential if the exchange rate moves enough in either direction. The value of a strangle option increases along with the volatility of the underlying currency pair.
Straddle Strategy: This is another type of option strategy and it consists in buying (long straddle) or selling (short straddle) both a call and a put option at the same strike price and for the same expiration date. A trader will get a long straddle option (buy) when he/she expects highly volatile market conditions. The value of a straddle option (premium) increases along with the volatility and the maturity of the underlying currency pair.
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Barrier Option: Barrier options belong to the category of exotic options – extremely popular among forex option traders – meaning that they possess a component other than the expiry date and the strike price. Regarding barrier options, the additional component is the trigger – or the barrier – which if reached either brings the option into being (knock in option) or cancels it (knock out option). You thus choose a strike price as well as a trigger. Since there is a chance that these options may never come into effect or may be canceled, they are generally cheaper that their vanilla counterpart.
Exotic options also include binary options which are based on a hypothetical scenario where you decide how much profit you want to make if the rate reaches a certain level.
Knock in: A knock-in option becomes a regular option (it is "knocked in”) if and when the trigger price is met before the expiration date. This means that if the rate is never reached, the contract is canceled and the buyer loses the premium. If the barrier rate is met, then the option starts running like a regular put or call option. Knock-in options are less expensive than regular options since they have an additional conditional component that cheapens the price of the premium. The further the barrier to the spot rate, the cheaper the premium, since there is a lesser chance that the option will be knocked in before the expiration date.
Knock out: The knock out option will automatically cease to exist and expire worthless (it will be "knocked out”) if and when the trigger price is reached before the expiration date. If the rate never hits the barrier, the knock out option runs the same way as a regular option. For a call knock-out option, the trigger is set below the spot rate, and above for a put (out-of-the-money). The higher the implied volatility, the greater the chance the barrier being triggered and the option being knocked out. Knock-out options are cheaper than regular put or call option (vanilla) since they may be knocked out before expiry. The premium gets cheaper as the barrier gets closer to the spot rate since the option has a greater chance of being knocked out.
Reverse knock in: The difference between a knock in option and a reverse knock in option lies in the localization of the trigger barrier. Whereas the trigger is out-of-the money for a knock in, it is in-the-money for a RKI.
Reverse knock out: The difference between a knock out option and a reverse knock out option lies in the localization of the trigger barrier. Whereas with a regular knock out, the trigger is set out-of-the-money (meaning below the spot rate for a call and above for a put), with a RKO, the trigger is set in-the-money (above the spot rate for a call and below for a put).
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Binary options: Binary options (also known as "rebate” options), are vanilla put and call options conditioned by something else other than just the price and the expiration date. They refer to conditional scenarios that if come true, either validate or invalidate the option. The trader fixes the amount of the desired payout he will get if his conditional scenario proves to be right. The price of the option or premium represents a percentage of that payout.
One Touch: When buying a one-touch option, traders set that if the currency trades at a specified rate (trigger), then he/she will receive a profit whose amount he has decided upon. He thus knows in advance the extent of his potential profit (payout) and loss (the premium).
No Touch: When buying this type of option, the trader sets that he/she will make profit (whose amount he/she sets) if and only if a currency rate does not reach
the specified trigger before a specified time. The further away the trigger from the spot rates, the lesser payout potential, since there is greater probability that the currency will not touch the strike rate.
Double One Touch: With this type of option, traders choose two triggers and set the profit they will make if either one is hit. Usually, double-one-touch options are used when traders expect highly volatile market conditions but don’t know what direction the market will take. In this sense, double one touch options are similar to long straddle or strangle options.
Double No Touch: Double no touch options are the opposite of the double one-touch options. Traders buy them when they expect a range-bound market with a relatively low volatility. In general, this type of option is profitable during the periods of consolidation that usually follow significant market moves.
Traders often combine various option types to build their option trading strategies. By associating different option types, some traders manage to minimize the risk they are taking. Some even claim to have found infallible methods. Others see it as a simple hedging instrument and use it to secure their funds.
1. Buyer of an option: The buyer of an option is the one who by paying the option premium buys the right but not the obligation exercises his option on t he seller/writer.
2. Wr i te r o f an op t ion :The w r i t e r o f a ca l l / pu t op t i on i s t he one who receives the option premium and is thereby obliged to sell/buy the asset if the buyer exercises on him.
3. Option price: Option price is the price, which the option buyer pays to the option seller. It is also referred as option premium.
4. Expiration date: The date specified in the options contract is known as expiration date, the exercise date, the strike date or the maturity.
5. Strike Price: The price specified in the options contract is known as strike price or the exercise price.
6. American options: these are the options that can be exercised at anytime upto the expiration date. Most exchange-traded options areAmericans.
7.European options: These are the options that can be exercised only on the expiration date itself. These are easier or analyze than American option, and properties of American options are frequently deducted from those of its European counterpart.8.In the money option :An in the money option is an option that would lead to a positive cash flow to the holder if it will exercise immediately. A call option in the index is set to be in-the-money when the current index stands at a level higher than the strike price (i.e. spot price>strike price). If the index is much higher than the strike price, the call is set to deep ITM. In the case of a put, the put is ITM if the index is below the strike price.
9.At-money option : (ATM)option is an option that would lead to zero cash flow if it were exercised immediately. An option on the index is at-the-money when the current index equals the strike price. 10.Out-of-the money option : (OTM)options is an option that would lead to a negative cash flow it was exercised immediately. A call option on the index is OTM when the current index stands at a level, which is less than t he strike price (spot price<strike price). If the index is much lower than the strike price, the call is set to be deep OTM. In the case of a put, the put is OTM if the index is above the strike price.
AMERICAN VS EUROPEAN OPTION:Its owner can exercise an American option at any time on or before the expiration date. A Eu ropean s t y l e op t i on g i ves t he owne r t he r i gh t t o use t he op t i on on l y on expiration date and not before.
Option Premium: A glance at the rights and obligations of buyer and seller reveals that option contracts are skewed. One way naturally wonder as to why the seller (writer) of an option would always be obliged to sell/buy an asset whereas the other party gets the right. The answer is that writer of an option receives, a consideration for Undertaking the obligation. This is known as the price or premium to the seller for the option. The buyer pays the premium for the option to the seller shelter he exercise the option is not exercised, it becomes worthless and the premium becomes the profit of the seller.
Factors Affecting Pricing:
1.Supply and demand in Secondary market2. Exercise price3. Risk free interest rate4. Volatility of underlying5. Time to expiration6. Dividend on underlying
Trading Strategies Involving Options
Unlike other derivatives (future, forward, swap), options provides flexibility (right to buy or sell an underlying instrument) in trading without any obligation. However, that’s flexibility comes with a cost. There are various techniques to estimate this cost, in other words price an option. I mentioned some of them in my previous blogs (Black Scholes, Monte Carlo, and Binomial Trees). In this blog, I will address on trading methods involving options. These methods are explained in great details in Options, Futures, and Other Derivatives by J. Hull and Derivatives Demystified by Andrew M. Chisholm.
Combination of Single Option and Stocks
This is the simplest strategies involving single option and underlying stock at same time. Please not in this text; we use European option in examples and these ideas can be used for American options too.For example, a portfolio consists of a long position in an underlying and a short position in the call option, which is called as “writing covered call” (Figure 1-a). This portfolio protects against sudden rise in underlying stock, which affects payoff short call in a negative way. Similarly, a portfolio with short position in underlying and long call (Figure 1-b) protects against sharp rises in short underlying.Other common single option strategy involves put options such as “protective put” (Figure 1-c) which consists of short underlying and put option. Short put option is protected with a short underlying. Long put option with long underlying (Figure 1-d) is used against sharp decline in the underlying.
SpreadsThis strategy involves of two or more options of same types and aims to profit from spreads caused by various combinations of strikes, maturity date and economical factors.
Bull SpreadsIf an investor would like to take advantage of increase in an underlying, this strategy would be used. Bull spreads employ two call options on same underlying with two different strike price (K1 and K2) . While option with higher K1 strike is shorted, other call option with lower K2 strike is longed in anticipation that in a bull market, the spread between K1 and K2 strike generates a profit. Table 1 and figure shows payoff from a bull spread strategy.
Bear SpreadsUnlike bear spread, if an underlying has potential to go down, bear spreads can be used. A short put option with lower K1 strike together with a long put option with higher K2 strike are used for bear spreads. Table 2 and figure 3 summarize the pay-off for bear spreads. Upside profit potential and downside risk is limited. Maximum payoff is K2-K1 spread when underlying price is less than K1.
Box SpreadsThis is a strategy used by arbitrage trader if an arbitrage opportunity occurs. Box spreads involves of bull and bear spreads with same K1 and K2 strike prices which generates always K2-K1 payoff, as table 3 illustrates. Therefore price of a box spread should be present value the payoff ((K2-K1)*exp(-rT)), if an arbitrage opportunity for investor is not wanted.
Butterfly SpreadsIn bear and bull spreads, investor positions himself/herself according to a potential upward or downward movement in underlying. On the other hand, in generic butterfly spread, investor positions himself/herself according to not volatile and moving underlying. In another words, if an investor thinks an underlying won’t go down nor up, he can buy butterfly spreads. Three different strike price with four call options are used: A long call with lower K1 strike price, and again a long call with higher K3 strike price and two short call with K2 strike (between K1 and K3, generally close to current underlying price (K3+K1)/2). As table 4 shows, if stock price stay close to around K2 a profit can be made. Butterfly spreads requires a small amount of cash investment at the beginning.
Butterfly spreads can be created with also put options: Two long put options with lower strike price K1 and higher strike price K3 and two short put options with strike price K2 which is between K1 and K3. If European put options are used, result will be same as call option’s butterfly spread.
One last point, butterfly spreads can be shorted or sold if it is thought an underlying goes either up or down but not sure which direction, which produces modest payoff if there is a major movement in any direction.
Calendar SpreadsSo far, in all spreads, the variant element was strike price and expire date was same. In calendar spreads, variant element is expire date and strike price is constant for all options. For example, a short call option with short-maturity and a long call option with relatively longer-maturity can be used to create a calendar spreads. Since, longer-maturity call option will cost more than short call option, an initial cash flow out happens. When short-maturity short option expires, long call option is sold. Similar to butterfly spreads, if underlying price stay close to strike price, investor will make profit. Otherwise, a loss is incurred.
Similar to butterfly spreads, put options can be used to construct calendar spreads. Strike price in a calendar spread is chosen according to trend of underlying. In bullish and bearish sentiment, higher and lower strike price is chosen, respectively.
Diagonal SpreadsIn this strategy, options with different strike and expiration date are used. Analyzing outcome of these strategies is more complex than other spread strategies. Advanced models are used to estimate payoff.
CombinationsIn this strategy, put and call options are used at same time with same underlying.
StraddleIn this common strategy, a put and call option are purchased with same strike and expiration date. Unlike butterfly strategy, if a significant movement in underlying price happens in any direction, this strategy produces a significant profit. Table 5 and Figure 6 depict payoff of straddle.
A reverse straddle can also be created selling put and call option with same strike price and expire date which is highly risky, if price of underlying changes significantly. On the other hand, similar to butterfly spreads, significant profit can be made if price of underlying is around strike price.
Strips and StrapsAs mentioned above, straddle is good if we are not certain about direction of movement in underlying. But if we have stronger tendency about direction of movement in one way but still not sure about direction like in straddle, strips and straps can be used. Strips and straps are kind of biased straddles. A strip consists of long call and two put options on same underlying with same strike price and expiry date. Similarly, a strap consists of long put and two call options on same underlying with same strike price and expiry date.
Strangles
In a strangle, an investor buys a put and call option with same expiration date with different strike prices. The strike price of put option (K1) is lower than the strike price of call option. This strategy is similar to straddles which bets on significant movement in underlying price(Figure 8). But in strangle, further movement is required for profit. But risk is lesser compare to straddle. Risk can be adjusted with strike prices K1 and K2. The further they are apart, the less the downside risk and the farther the underlying price has to move to make a profit.
Basic option positions:
The four basic strategies of options are:
Long call
Long put
Short call
Short put
Calls and Puts Diagrams
Call Options and Put Options Diagram
How do we use them and how can they be replicated synthetically?
Long Call
The long call is one of the most simple and popular basic strategies for options. Long call is a bullish strategy since it involves in buying a call option in the expectation that price will rise.
A long call can be replicated synthetically by a long underlying asset transaction and a long put option.
As time passes, the value of a long call option erodes toward expiration value. If the volatility increases, erosion slows. Conversely, as volatility decreases, erosion speeds up.
Buying a call gives you the right to buy the underlying stock at the strike price any time until expiry.
Long Call (Buy a Call)
You would buy a call if you think the price of the underlying stock is going to rise (when you are bullish on the underlying stock).
Figure 4 shows the risk return involved with buying a call with a strike price of $25 for a premium of $5. When you buy a call the most you can lose is the premium you paid for the call. However there is unlimited profit if the underlying stock moves up.
If the price of the stock rose to $40 by the expiry date the call option would be worth $15 ($40 the stock price - $25 the strike price). In this example the holder of the call option would have a profit of $10 ($15 the value of the option at expiry - $5 the premium paid for the option).
Long Put
If the trader expects the market is on the fall, he will make profit by buying a put option. As the market falls, the profit of the put option increases.
A long put can be replicated synthetically by a short underlying asset transaction and a long call option. Buying a put gives you the right to sell the underlying stock at the strike price any time until expiry.
Long Put
When you buy a put to open a position you are said to be "long a put". You can buy a put either to speculate or to protect a position.
Speculative Put
A speculative put is when you buy a put in hopes that the stock will fall, as opposed to buying a put to protect a position in the underlying stock.
Figure 7 shows the risk and return involved with buying a put (speculative put) with a strike price of $25 for a premium of $5. When you buy a put the most you can lose is the premium you pay for buying the put option. However you are able to make large profits if the underlying stock falls.
Figure 7.
If the price of the stock fell to $10 by the expiry date, the put option would have a value of $15 ($25 strike price that you could sell the stock for - $10 current stock price that you could buy the stock for). In this example the put holder would have a $10 profit ($15 the value of the option at expiry - $5 the premium paid for the option).
Protective Put
A protective put is when you have a position in the underlying stock and you buy a put to protect against a drop in the stock's price. A protective put is like buying an insurance policy on your stock to protect against the drop in price. You may want to buy a protective put if you think the underlying stock is going to rise buy you have some short term concerns, and you want to protect yourself in case there is a sharp drop in the stock price.
Figure 8 shows the risk and return involved with holding a stock and buying a protective put on it. When you buy a protective put you still have unlimited profit potential while you are able to limit your risk.
Figure 8.
If the price of the underlying stock fell to $25 or lower by the expiry date the combined position would have a loss of $10 (this remains the same because the profits on the put option will offset any losses on the stock below the $25 strike price). If the price of the
underlying stock went up to $45 there would be a profit of $10 ($15 the gain on the stock - $5 the premium paid to buy the protective put).
A protective put has the same risk reward profile as buying a call option.
Short Call
A short call is the opposite position to the long call. The seller sells the option because he believes the market is going down.
A long call can be replicated synthetically by a short underlying asset transaction and a short put option.
Writing a call obligates you to sell the underlying stock at the strike price any time until expiry if you are assigned.
Short Call
You short a call when you write (sell) a call that you don't currently own. There are two basic types of short calls covered and uncovered (naked).
Naked Call (Uncovered Call)
You could write a call if you think the price of the underlying stock is going to stay the same or fall (when you are neutral or bearish on the underlying stock).
Figure 5 shows the risk and return involved with writing a naked call with a strike price of $25 for a premium of $5. When you write a naked call the most you can make is the premium you receive for writing the call. However you are taking on unlimited risk if the underlying stock moves up.
If the price of the stock rose to $40 by the expiry date the naked call position would be in a loss of $10 ($5 premium you originally received for writing the naked call + $25 the strike price which you are obligated to sell the stock for - $40 the price you would have to buy the stock for).
Covered Call
A covered call is when you own the underlying stock and you write a call. The call is covered because if you get assigned and have to sell the underlying stock it is OK because you already own it. If you think that a stocks price will stay the same or move up slightly you could write a covered call.
Figure 6 shows the risk and return involved with writing a covered call with a strike price of $25 for a premium of $3 at a time when the underlying stock is trading at $22. When you write a covered call there is a maximum amount that you can make. However you are taking on a lot of risk if the underlying stock falls.
Figure 6.
If the price of the underlying stock rose to $25 or higher by the expiry date the overall position would have a profit of $6 (this remains the same because any profits on the stock are offset by losses on the short call). If the price of the underlying stock fell to $10 your combined loss would be $9 ($10 the current price of the stock - $22 the price paid for the stock + $3 the premium received for writing the call).
A covered call position has the same risk reward profile as writing a naked put
Short Put
A short put is implemented by traders who believe that market is going up. It is the opposite position of people who is bearish about the market.
A short put can be replicated synthetically by a long underlying asset transaction and a short call option.
Writing a put obligates you to buy the underlying stock at the strike price any time until expiry if you are assigned.
Short Put (Writing a Put)
When you write (sell) a put that you don't already own you are said to be "short a put". You could write a put if you think the price of the underlying stock is going to stay the same or rise (when you are neutral or bullish on the underlying stock).
Figure 9 shows the risk and return involved with writing a put with a strike price of $25 for a premium of $5. When you write a put the most you can make is the premium you receive for writing the put option. However you are taking on the risk of large losses if the underlying stock falls.
Figure 9.
If the price of the stock fell to $5 by the expiry date, the put option would have a value of -$20 ($5 current stock price that you could sell the stock for - $25 strike price that you would have to buy the stock for). In this example the put writer would have a $15 loss ($5 the premium received for writing the option - $20 the value of the option you wrote at expiry).
Writing a put has the same risk reward profile as a covered call position.
Naked Put (Uncovered) vs. Short Put Covered by Cash
There are two basic types of short puts covered and uncovered (naked).
When you write a put you are taking on an obligation to buy the underlying stock at the strike price. You can cover this obligation by having enough cash to buy the shares at the strike price. There are several other methods of covering a short put that will be discussed in the Interval Shift Self-Study Online Seminar. If you write a put option that is not covered you are taking on more risk, this is called a naked or an uncovered put.
Summary of Basic Option Strategies
Position Summary
Buy a Call(Long Call)
You pay a premium for the right to buy the stock at the strike price.
Sell a Call(Short Call)
You get a premium for taking on the obligation to sell a stock you don't own at the strike price.
Sell a Covered Call You get a premium for taking on the obligation to sell a stock that you own at the strike price.
Buy a Put(Long Put)
You pay a premium for the right to sell a stock you don't own at the strike price.
Buy a Protective Put You pay a premium for the right to sell a stock that you own at the strike price.
Sell a Covered Put(Short Put)
You get a premium for taking on the obligation to buy a stock at the strike price.
Natural Vs Synthetic Strategies
Natural Strategy Synthetic Strategy
Long Call = Long underlying and long put
Long Put = Short underlying and long call
Short Call = Short underlying and short put
Short Put = Long underlying and short call
Long underlying = Long call and short put
Short underlying = Short call and long put
Unit-4
Options Pricing
The premium of an option has two main components: intrinsic value and time value.
Intrinsic Value (Calls):
When the underlying security's price is higher than the strike price a call option is said to be "in-the-money."
Intrinsic Value (Puts):
If the underlying security's price is less than the strike price, a put option is "in-the-money." Only in-the-money options have intrinsic value, representing the difference between the current price of the underlying security and the option's exercise price, or strike price.
Time Value:
Prior to expiration, any premium in excess of intrinsic value is called time value. Time value is also known as the amount an investor is willing to pay for an option above its intrinsic value, in the hope that at some time prior to expiration its value will increase because of a favorable change in the price of the underlying security. The longer the amount of time for market conditions to work to an investor's benefit, the greater the time value.
Six Major Factors Influencing Options Premium
There are six major factors that influence option premiums. The factors having the greatest effect are:
A change in price of the underlying security Strike price
Time until expiration
Volatility of the underlying security
Dividends/Risk-free interest rate Dividends and risk-free interest rate have a lesser effect.
Changes in the underlying security price can increase or decrease the value of an option. These price changes have opposite effects on calls and puts. For instance, as the value of the underlying security rises, a call will generally increase and the value of a put will generally decrease in price. A decrease in the underlying security's value will generally have the opposite effect.
The strike price determines whether or not an option has any intrinsic value. An option's premium (intrinsic value plus time value) generally increases as the option becomes further in the money, and decreases as the option becomes more deeply out of the money.
Time until expiration, as discussed above, affects the time value component of an option's premium. Generally, as expiration approaches, the levels of an option's time value, for both puts and calls, decreases or "erodes." This effect is most noticeable with at-the-money options.
The effect of volatility is the most subjective and perhaps the most difficult factor to quantify, but it can have a significant impact on the time value portion of an option's premium. Volatility is simply a measure of risk (uncertainty), or variability of price of an option's underlying security. Higher volatility estimates reflect greater expected fluctuations (in either direction) in underlying price levels. This expectation generally results in higher option premiums for puts and calls alike, and is most noticeable with at-the-money options.
The effect of an underlying security's dividends and the current risk-free interest rate have a small but measurable effect on option premiums. This effect reflects the "cost of carry" of shares in an underlying security -- the interest that might be paid for margin or received from alternative investments (such as a Treasury bill), and the dividends that would be received by owning shares outright.
Options trading uses several related phrases that are unique to options markets. Some commonly used, but often misunderstood options phrases are :
Strike Price
The strike price (or exercise price) of an options contract is the price that the underlying security will be bought or sold at if the option is exercised (i.e. if the rights given by the
contract are used). It is the difference between the strike price and the price of the underlying security at the time of exercise that gives the options trader their profit.
Exercise
An option is exercised if the rights given to the buyer of the options contract are used. For example, if the buyer of a Call contract decides to use their right to buy the underlying security on (European style options) or at any time up to (US style options) the expiration date, they will have exercised their option. Options contracts are exercised via the exchange or options clearing system, at which time a matching options seller is chosen (by the exchange) and becomes obligated to complete the transaction.
Expiration Date
Options contracts specify the expiration date as part of the contract specifications. For European style options, the expiration date is the date that an in the money (in profit) options contract will be exercised. For US style options, the expiration date is the last date that an in the money options contract can be exercised. Any options contracts that are out of the money (not in profit) on the expiration date will not be exercised, and will expire worthless instead. Options traders who have bought options contracts want their options to be in the money on the expiration date, and traders who have sold options contracts want their options to be out of the money and expire worthless on the expiration date.
Options Expiration
Expiration date is the day on which an options contract is no longer valid and, therefore, ceases to exist.
Options expiration is one of the most important parameters of the options. All options have expiration date at with they expire. That is the main difference between options and stock. The options are not traded after they expired. A trader who owns an option has the right to exercise this option any time before or at the expiration date (American style options) but not after.
The expiration date for all listed options in the U.S. is the third Friday of the expiration month (except when it falls on a holiday, in which case it is on Thursday). A trader who has in-the money options on their expiration date has to make a decision whether to exercise them or not. Out-of-the-money options on the expiry date are worthless.
Basically you have to remember that at the end of expiration date:
all call options (out-of-the-money) whose strike prices are above the price of the underlying stock or index will expire worthless;
all put options (out-of-the-money) whose strike prices are below the price of the underlying stock or index will expire worthless;
all call options (in-the-money) whose strike prices are below the price of the underlying stock or index could be exercised;
all put options (in-the-money) whose strike prices are above the price of the underlying stock or index could be exercised.
The expiration date is the main factor that affects the price of the options. The closer it is to the expiration the cheaper the options would be. For instance, a trader who decided to buy SPY call options with January expiration and $140 strike price would pay less if the same trader decided to by the same strike ($140) SPY call options but with February expiration.
An option trader always has to remember that time decay affect options price. Even if the underlying stock stays at the same price the options on this stock would become cheaper with time.
Option lose it's value with time!
For instance, you bought QQQQ calls for $2 per contacts when QQQQ market price was $45 per share. Even if in a month QQQQ is back at $45 level the same QQQQ calls may cost $1 per contract now.
Strike Price
The strike price is the price at which a option contract can be exercised.
The strike prices are fixed in the contract. For call options, the strike price is the price at which the underlying stock could be bought (up to the expiration date) and for put options the strike price is the price at which underlying stock could be sold.
The strike price is one of the most important factors in the options pricing. At the expiration date the difference between the underlying stock current market price and the option's strike price represents the amount of profit per share gained upon the exercise. Of course this is true for options that are in the money.
Put-call parity relationship
The relationship between the price of a put and the price of a call on the same underlying security with the same expiration date, which prevents arbitrage opportunities. Holding the stock and buying a put will deliver the exact payoff as buying one call and investing the present value (PV) of the exercise price. The call value equals C=S+P-PV(k).
C - P = S -X + i - dWhere:C = Call option priceP = Put option PriceS = Stock priceX = exercise pricei = cost of carry d = present value of dividends This relationship between the Put, Call and stock prices originally appeared in a paper by Hans Stoll entitled "The Relationship Between Put and Call Prices" in 1969. The formula was developed for European options (those are the ones that can't be exercised early) but it also applies pretty well to American options. The reason is because unless one of the options is really deep in the money or the dividend is extremely large, the value of the early exercise component in the American style options is generally small and doesn't have much impact on the formula.In my opinion, it is very important that you understand this basic relationship between Puts, Calls and Stock. I am constantly amazed when I talk to people who have been trading options for any significant length of time and I realize that they don't know there is a connection between the prices. I guess on one level that's okay, it helps me pay my son's college tuition!Let's see how to calculate the i and d terms, and then we will apply the formula to some examples. The cost of carry, i, is calculated by multiplying the risk free rate of return by the exercise price times the number of days to expiration divided by 365. For our purposes, this risk free rate is what you can get on an investment with only a minute possibility of default, such as short term CD's. Traders, I know have recently been using about 5%, although after the last 2 rate cuts, perhaps a lower rate like 4.5% may be more appropriate. To calculate the d, we must take into account any dividends that are being paid prior to expiration and calculate their present value. All that means is we must divide the dividend amount by (1 + risk free interest rate) raised to a power. That power is the time to expiration divided by 365. By the way, since the dividend amount is usually small relative to the stock price and with interest rates being as low as they currently are, most traders just use the actual dividend amount instead of the present value of the dividend, in the formula. It has a minimal effect on the prices. Let's say we know the following about XYZ stock and options: It's trading @ $52, and doesn't pay a dividendThere are 37 days to Jan expiration The Jan 50 Call is trading @ 5.50My risk free rate of return is 5%The question is, how much should the Jan 50 Put be trading for?First, calculate i as .05 x 50 x (37/365) = .25 We also know that d = 0, so our equation
becomes;C - P = S - X + i - dOr 5.50 - P = 52 - 50 + .25 - 05.50 - P = 2.25Finally, we get P = 3.25 Just for fun, let's assume that XYZ did have a 40¢ dividend that was payable in 25 days. I would calculate the present value of the dividend as .40/(1.05)^(25/365) = .399, i.e. .40 (Now it should be apparent why traders would just use the value of the dividend.) Substituting .40 for d in the above equation and solving, we get P = 3.65. In a like manner, we could calculate the Call if we knew the Put price, or for that matter the Stock price, if we knew where the Put and Call were trading.Okay, this is all very nice, but now that I know it, how do I use it in my trading? That's the $497,097 question ($64,000 increased for inflation.) First, you should feel good knowing that you know and understand something that probably 80% of non-professional options traders don't know. Second, if the prices are out of line, then something may be going on. You may not be able to short the stock, or it may be hard to borrow, or some corporate action such as a merger or takeover may be pending. Finally, if none of these things apply, and the prices are out of line, there is a way to capture the difference. If the Put is trading for less than the equation says it should be, relative to the Call, we can buy the Put, sell the Call and then lock up our profit by buying stock. Similarly, if the Call is undervalued relative to where the Put is trading, we can buy the Call, sell the Put, and again, lock in the profit by shorting the stock. These positions are called Conversions and Reverse Conversions (or Reversals), respectively. A future article will describe in detail how these positions lock in the profit, but for now it would be educational for you to think about it. Oh, before you get too excited about finding these pricings and making lots of money, you should realize that they don't come along all that often anymore. Also, when they do appear, it's only for a short time, so you have to react quickly, since selling the overpriced options and buying the under priced options brings the prices back into line rather quickly.
Option Pricing Models
The Black-Scholes model and the Cox, Ross and Rubinstein binomial model are the primary pricing models used by the software available from this site. Both models are based on the same theoretical foundations and assumptions (such as the geometric Brownian motion theory of stock price behaviour and risk-neutral valuation). However, there are also some some important differences between the two models and these are highlighted below. Black–Scholes:
The Black–Scholes model (pronounced /ˌblæk ˈʃoʊlz/ [1] ) is a mathematical description
of financial markets and derivative investment instruments. The model allows derivation
of the Black–Scholes formula, which allows the precise pricing of European-
style options. The formula led to a boom in options trading and the creation of
the Chicago Board Options Exchange. While much criticized, by those inside and
outside the financial industry, the formula is still widely used, in part due to its ease-of-
use and reliability in many situations.
The model was first articulated by Fischer Black and Myron Scholes in their 1973 paper,
"The Pricing of Options and Corporate Liabilities." The foundation for their research
relied on work developed by scholars such as Jack L. Treynor, Paul Samuelson, A.
James Boness, Sheen T. Kassouf, and Edward O. Thorp.[2][citation needed] They derived
a partial differential equation, now called the Black-Scholes PDE, which governs the
price of the option over time. The key idea behind the derivation was to perfectly hedge
(finance) the option by buying and selling the underlying asset in just the right way and
consequently "eliminate risk". This hedge is called delta hedging and is the basis of
more complicated hedging strategies such as those engaged in by Wall
Street investment banks. The hedge implies there is only one right price for the option
and is given by the Black-Scholes formula.
Robert C. Merton was the first to publish a paper expanding the mathematical
understanding of the options pricing model and coined the term Black–Scholes options
pricing model. Merton and Scholes received the 1997 Nobel Prize in Economics (The
Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel) for their
work. Though ineligible for the prize because of his death in 1995, Black was mentioned
as a contributor by the Swedish academy.[3]
Model assumptions
he Black–Scholes model of the market for a particular equity makes the following
explicit assumptions:
It is possible to borrow and lend cash at a known constant risk-free interest rate.
There is no arbitrage opportunity.
The underlying security does not pay a dividend.[4]
The stock price follows a geometric Brownian motion with constant drift
and volatility.
All securities are infinitely divisible (i.e., it is possible to buy any fraction of a
share).
There are no restrictions on short selling.
There are no transaction costs, taxes or bid-ask spread.
From these conditions in the market for an equity (and for an option on the equity), the
authors show that "it is possible to create a hedged position, consisting of a long
position in the stock and a short position in [calls on the same stock], whose value will
not depend on the price of the stock."[5]
Several of these assumptions of the original model have been removed in subsequent
extensions of the model. Modern versions account for changing interest rates (Merton,
1976)[citation needed], transaction costs and taxes (Ingersoll, 1976)[citation needed], and dividend
payout (Merton, 1973)[citation needed].
The Black-Scholes model is used to calculate a theoretical call price (ignoring dividends paid during the life of the option) using the five key determinants of an option's price: stock price, strike price, volatility, time to expiration, and short-term (risk free) interest rate.
The original formula for calculating the theoretical option price (OP) is as follows:
Where:
The variables are:
S = stock priceX = strike pricet = time remaining until expiration, expressed as a percent of a yearr = current continuously compounded risk-free interest ratev = annual volatility of stock price (the standard deviation of the short-term returns over one year). See below for how to estimate volatility. ln = natural logarithmN(x) = standard normal cumulative distribution functione = the exponential function
(Or)
The Black Scholes formula calculates the price of European put and call options. It can
be obtained by solving the Black–Scholes stochastic differential equation.
The value of a call option for a non-dividend paying underlying stock in terms of the
Black–Scholes parameters is:
Also,
The price of a corresponding put option based on put-call parity is:
For both, as above:
is the cumulative distribution function of the standard normal
distribution
T − t is the time to maturity
S is the spot price of the underlying asset
K is the strike price
r is the risk free rate (annual rate, expressed in terms of continuous
compounding)
σ is the volatility of returns of the underlying asset
Interpretation
The terms N(d1),N(d2) are the probabilities of the option expiring in-the-money under the
equivalent exponential martingale probability measure (numéraire=stock) and the
equivalent martingale probability measure (numéraire=risk free asset), respectively. The
equivalent martingale probability measure is also called the risk-neutral probability
measure. Note that both of these are probabilities in a measure theoretic sense, and
neither of these is the true probability of expiring in-the-money under the real probability
measure. To calculate the probability under the real ("physical") probability measure,
additional information is required—the drift term in the physical measure, or
equivalently, the market price of risk.
Derivation
We now show how to get from the general Black–Scholes PDE to a specific valuation
for an option. Consider as an example the Black–Scholes price of a call option, for
which the PDE above has boundary conditions
The last condition gives the value of the option at the time that the option matures. The
solution of the PDE gives the value of the option at any earlier
time, . To solve the PDE we transform the equation into
a diffusion equation which may be solved using standard methods. To this end we
introduce the change-of-variable transformation
Then the Black–Scholes PDE becomes a diffusion equation
The terminal condition C(S,T) = max{S − K,0} now becomes an initial condition
Using the standard method for solving a diffusion equation we have
which after a some manipulations yields
where
Reverting u,x,τ to the original set of variables yields the above stated solution to the
Black–Scholes equation.
Advantages & Limitations:
Advantage: The main advantage of the Black-Scholes model is speed -- it lets you calculate a very large number of option prices in a very short time.
Limitation: The Black-Scholes model has one major limitation: it cannot be used to accurately price options with an American-style exercise as it only calculates the option price at one point in time -- at expiration. It does not consider the steps along the way where there could be the possibility of early exercise of an American option.
As all exchange traded equity options have American-style exercise (ie they can be exercised at any time as opposed to European options which can only be exercised at expiration) this is a significant limitation.
The exception to this is an American call on a non-dividend paying asset. In this case the call is always worth the same as its European equivalent as there is never any advantage in exercising early.
Various adjustments are sometimes made to the Black-Scholes price to enable it to approximate American option prices (eg the Fischer Black Pseudo-American method) but these only work well within certain limits and they don't really work well for puts.
Binomial Option Pricing Model:In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein (1979). Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument. In general, binomial options pricing models do not have closed-form solutions.
Use of the model
The Binomial options pricing model approach is widely used as it is able to handle a
variety of conditions for which other models cannot easily be applied. This is largely
because the BOPM is based on the description of an underlying instrument over a
period of time rather than a single point. As a consequence, it is used to value American
options that are exercisable at any time in a given interval as well asBermudan
options that are exercisable at specific instances of time. Being relatively simple, the
model is readily implementable in computersoftware (including a spreadsheet).
Although computationally slower than the Black-Scholes formula, it is more accurate,
particularly for longer-dated options on securities withdividend payments. For these
reasons, various versions of the binomial model are widely used by practitioners in the
options markets.
For options with several sources of uncertainty (e.g., real options) and for options with
complicated features (e.g., Asian options), binomial methods are less practical due to
several difficulties, and Monte Carlo option models are commonly used instead. Monte
Carlo simulation is computationally time-consuming, however (cf. Monte Carlo methods
in finance).
Methodology
The binomial pricing model traces the evolution of the option's key underlying variables
in discrete-time. This is done by means of a binomial lattice (tree), for a number of time
steps between the valuation and expiration dates. Each node in the lattice represents a
possible price of the underlying at a given point in time.
Valuation is performed iteratively, starting at each of the final nodes (those that may be
reached at the time of expiration), and then working backwards through the tree towards
the first node (valuation date). The value computed at each stage is the value of the
option at that point in time.
Option valuation using this method is, as described, a three-step process:
1. price tree generation,
2. calculation of option value at each final node,
3. sequential calculation of the option value at each preceding node.
STEP 1: Create the binomial price tree
The tree of prices is produced by working forward from valuation date to expiration.
At each step, it is assumed that the underlying instrument will move up or down by a
specific factor (u or d) per step of the tree (where, by definition, and ).
So, if S is the current price, then in the next period the price will either be
or .
The up and down factors are calculated using the underlying volatility, σ, and the time
duration of a step, t, measured in years (using the day count convention of the
underlying instrument). From the condition that the variance of the log of the price is σ2t,
we have:
The above is the original Cox, Ross, & Rubinstein (CRR) method; there are other
techniques for generating the lattice, such as "the equal probabilities" tree.
The Trinomial tree is a similar model, allowing for an up, down or stable path.
The CRR method ensures that the tree is recombinant, i.e. if the underlying asset
moves up and then down (u,d), the price will be the same as if it had moved down and
then up (d,u) — here the two paths merge or recombine. This property reduces the
number of tree nodes, and thus accelerates the computation of the option price.
This property also allows that the value of the underlying asset at each node can be
calculated directly via formula, and does not require that the tree be built first. The node-
value will be:
Where Nu is the number of up ticks and Nd is the number of down ticks.
STEP 2: Find Option value at each final node
At each final node of the tree — i.e. at expiration of the option — the option value is
simply its intrinsic, or exercise, value.
Max [ (Sn − K), 0 ], for a call option
Max [ (K – Sn), 0 ], for a put option:
Where K is the strike price and Sn is the spot price of the
underlying asset at the nth period.
STEP 3: Find Option value at earlier nodes
Once the above step is complete, the option value is then found for each node, starting
at the penultimate time step, and working back to the first node of the tree (the valuation
date) where the calculated result is the value of the option.
In overview: the "binomial value" is found at each node, using the risk
neutrality assumption; see Risk neutral valuation. If exercise is permitted at the node,
then the model takes the greater of binomial and exercise value at the node.
The steps are as follows:
1) Under the risk neutrality assumption, today's fair price of a derivative is equal to
the expected value of its future payoff discounted by therisk free rate. Therefore,
expected value is calculated using the option values from the later two nodes (Option
up and Option down) weighted by their respective probabilities -- "probability" p of an up
move in the underlying, and "probability" (1-p) of a down move. The expected value is
then discounted at r, the risk free rate corresponding to the life of the option.
The following formula to compute the expectation value is applied at each node:
Binomial Value = [ p × Option up + (1-p) × Option down] × exp (- r × Δt), or
where
is the option's value for the node at time ,
is chosen such that the related binomial
distribution simulates the geometric Brownian motion of the underlying stock with
parameters r and σ,
q is the dividend yield of the underlying corresponding to the life of the option. It
follows that in a risk-neutral world futures price should have an expected growth
rate of zero and therefore we can consider q = r for futures.
Note that for p to be in the interval (0,1) the following condition on Δt has to be
satisfied .
(Note that the alternative valuation approach, arbitrage-free pricing, yields identical
results; see "delta-hedging".)
2) This result is the "Binomial Value". It represents the fair price of the derivative at a
particular point in time (i.e. at each node), given the evolution in the price of the
underlying to that point. It is the value of the option if it were to be held — as opposed to
exercised at that point.
3) Depending on the style of the option, evaluate the possibility of early exercise at each
node: if (1) the option can be exercised, and (2) the exercise value exceeds the
Binomial Value, then (3) the value at the node is the exercise value.
For a European option, there is no option of early exercise, and the binomial
value applies at all nodes.
For an American option, since the option may either be held or exercised prior to
expiry, the value at each node is: Max (Binomial Value, Exercise Value).
For a Bermudan option, the value at nodes where early exercise is allowed is:
Max (Binomial Value, Exercise Value); at nodes where early exercise is not
allowed, only the binomial value applies.
In calculating the value at the next time step calculated - i.e. one step closer to valuation
- the model must use the value selected here, for "Option up" / "Option down" as
appropriate, in the formula at the node.
Advantages & Limitations:
Advantage: The big advantage the binomial model has over the Black-Scholes model is that it can be used to accurately price American options. This is because with the binomial model it's possible to check at every point in an option's life (ie at every step of the binomial tree) for the possibility of early exercise (eg where, due to eg a dividend, or a put being deeply in the money the option price at that point is less than its intrinsic value).
Where an early exercise point is found it is assumed that the option holder would elect to exercise, and the option price can be adjusted to equal the intrinsic value at that point. This then flows into the calculations higher up the tree and so on.
The on-line binomial tree graphical option calculator highlights those points in the tree structure where early exercise would have have caused an American price to differ from a European price.
The binomial model basically solves the same equation, using a computational procedure that the Black-Scholes model solves using an analytic approach and in doing so provides opportunities along the way to check for early exercise for American options.
Limitation: The main limitation of the binomial model is its relatively slow speed. It's great for half a dozen calculations at a time but even with today's fastest PCs it's not a practical solution for the calculation of thousands of prices in a few seconds.
Relationship to the Black-Scholes model
The same underlying assumptions regarding stock prices underpin both the binomial and Black-Scholes models: that stock prices follow a stochastic process described by geometric brownian motion. As a result, for European options, the binomial model converges on the Black-Scholes formula as the number of binomial calculation steps increases. In fact the Black-Scholes model for European options is really a special case of the binomial model where the number of binomial steps is infinite. In other words, the binomial model provides discrete approximations to the continuous process underlying the Black-Scholes model.
Whilst the Cox, Ross & Rubinstein binomial model and the Black-Scholes model ultimately converge as the number of time steps gets infinitely large and the length of each step gets infinitesimally small this convergence, except for at-the-money options, is anything but smooth or uniform. To examine the way in which the two models converge see the on-line Black-Scholes/Binomial convergence analysis calculator. This lets you examine graphically how convergence changes as the number of steps in the binomial calculation increases as well as the impact on convergence of changes to the strike price, stock price, time to expiration, volatility and risk free interest rate.
Unit-5
What is a swap?
A swap is nothing but a barter or exchange but it plays a very important role in
international finance. A swap is the exchange of one set of cash flows for another. A
swap is a contract between two parties in which the first party promises to make a
payment to the second and the second party promises to make a payment to the first.
Both payments take place on specified dates. Different formulas are used to determine
what the two sets of payments will be. In finance, a swap is a derivative in
which counterparties exchange certain benefits of one party's financial instrument for
those of the other party's financial instrument. The benefits in question depend on the
type of financial instruments involved. For example, in the case of a swap involving
two bonds, the benefits in question can be the periodic interest (or coupon) payments
associated with the bonds. Specifically, the two counterparties agree to exchange one
stream of cash flows against another stream. These streams are called the legs of the
swap. The swap agreement defines the dates when the cash flows are to be paid and
the way they are calculated.[1] Usually at the time when the contract is initiated at least
one of these series of cash flows is determined by a random or uncertain variable such
as an interest rate, foreign exchange rate, equity price or commodity price.[1]
The cash flows are calculated over a notional principal amount, which is usually not
exchanged between counterparties. Consequently, swaps can be in cash or collateral.
Swaps can be used to hedge certain risks such as interest rate risk, or to speculate on
changes in the expected direction of underlying prices.
The first swaps were negotiated in the early 1980s.[1] David Swensen, a Yale Ph.D. at
Salomon Brothers, engineered the first swap transaction according to "When Genius
Failed: The Rise and Fall of Long-Term Capital Management" by Roger Lowenstein.
Today, swaps are among the most heavily traded financial contracts in the world: the
total amount of interest rates and currency swaps outstanding is more thаn $426.7
trillion in 2009, according to International Swaps and Derivatives Association (ISDA).
Swap market:
Most swaps are traded over-the-counter (OTC), "tailor-made" for the counterparties.
Some types of swaps are also exchanged on futures markets such as the Chicago
Mercantile Exchange Holdings Inc., the largest U.S. futures market, the Chicago Board
Options Exchange, IntercontinentalExchange and Frankfurt-based Eurex AG.
Classification of swaps is done on the basis of what the payments are based on. The different types of swaps are as follows.
Interest rate swaps
Currency Swaps
Commodity swaps
Equity swaps
Interest rate swapsThe interest rate swap is the most frequently used swap. An interest rate swap generally involves one set of payments determined by the Eurodollar (LIBOR) rate. Although, it can be pegged to other rates. The other set is fixed at an agreed-upon rate. This other agreed upon rate usually corresponds to the yield on a Treasury Note with a comparable maturity. Although, this can also be variable.
Additionally, there will be a spread of a pre-determined amount of basis points. This is just one type of interest rate swap. Sometimes payments tied to floating rates are used for interest rate swaps. The notional principal is the exchange of interest payments based on face value. The notional principal itself is not exchanged. On the day of each payment, the party who owes more to the other makes a net payment. Only one party makes a payment.
Currency swapsA currency swap is an agreement between two parties in which one party promises to make payments in one currency and the other promises to make payments in another currency. Currency swaps are similar yet notably different from interest rate swaps and are often combined with interest rate swaps.
Currency swaps help eliminate the differences between international capital markets. Interest rates swaps help eliminate barriers caused by regulatory structures. While currency swaps result in exchange of one currency with another, interest rate swaps help exchange a fixed rate of interest with a variable rate. The needs of the parties in a swap transaction are diametrically different. Swaps are not traded or listed on exchange but they do have an informal market and are traded among dealers.
A swap is a contract, which can be effectively combined with other type of derivative instruments. An option on a swap gives the party the right, but not the obligation to enter into a swap at a later date.
Commodity swapsIn commodity swaps, the cash flows to be exchanged are linked to commodity prices. Commodities are physical assets such as metals, energy stores and food including cattle. E.g. in a commodity swap, a party may agree to exchange cash flows linked to prices of oil for a fixed cash flow.
Commodity swaps are used for hedging against
Fluctuations in commodity prices or
Fluctuations in spreads between final product and raw material prices (E.g. Cracking spread which indicates the spread between crude prices and refined product prices significantly affect the margins of oil refineries)
A Company that uses commodities as input may find its profits becoming very volatile if the commodity prices become volatile. This is particularly so when the output prices may not change as frequently as the commodity prices change. In such cases, the company would enter into a swap whereby it receives payment linked to commodity prices and pays a fixed rate in exchange. A producer of a commodity may want to reduce the variability of his revenues by being a receiver of a fixed rate in exchange for a rate linked to the commodity prices.
Equity swapsUnder an equity swap, the shareholder effectively sells his holdings to a bank, promising to buy it back at market price at a future date. However, he retains a voting right on the shares.
COMPONENTS OF SWAP PRICE
What are the components of a swap price?There are four major components of a swap price.
Benchmark price Liquidity (availability of counter parties to offset the swap).
Transaction cost
Credit risk
Benchmark price: Swap rates are based on a series of benchmark instruments. They may be quoted as a spread over the yield on these benchmark instruments or on an absolute interest rate basis. In the Indian markets the common benchmarks are MIBOR, 14, 91, 182 & 364 day T-bills, CP rates and PLR rates.
Liquidity: Liquidity, which is function of supply and demand, plays an important role in swaps pricing. This is also affected by the swap duration. It may be difficult to have counterparties for long duration swaps, especially so in India.
Transaction Costs: Transaction costs include the cost of hedging a swap. Say in case of a bank, which has a floating obligation of 91 day T. Bill. Now in order to hedge the bank would go long on a 91 day T. Bill. For doing so the bank must obtain funds. The transaction cost would thus involve such a difference.
Yield on 91 day T. Bill - 9.5%
Cost of fund (e.g.- Repo rate) – 10%
The transaction cost in this case would involve 0.5%
Credit Risk: Credit risk must also be built into the swap pricing. Based upon the credit rating of the counterparty a spread would have to be incorporated. Say for e.g. it would be 0.5% for an AAA rating.
Variance swap
A variance swap is an over-the-counter financial derivative that allows one
to speculate on or hedge risks associated with the magnitude of movement,
i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock
index.
One leg of the swap will pay an amount based upon the realised variance of the price
changes of the underlying product. Conventionally, these price changes will be
daily log returns, based upon the most commonly used closing price. The other leg of
the swap will pay a fixed amount, which is the strike, quoted at the deal's inception.
Thus the net payoff to the counterparties will be the difference between these two and
will be settled in cash at the expiration of the deal, though some cash payments will
likely be made along the way by one or the other counterparty to maintain agreed
upon margin.
Structure and features
The features of a variance swap include:
the variance strike
the realised variance
the vega notional: Like other swaps, the payoff is determined based on
a notional amount that is never exchanged. However, in the case of a variance
swap, the notional amount is specified in terms of vega, to convert the payoff into
dollar terms.
The payoff of a variance swap is given as follows:
where:
Nvar = variance notional (a.k.a. variance units),
= annualised realised variance, and
= variance strike.[1]
The annualised realised variance is calculated based on a prespecified set of sampling
points over the period. It does not always coincide with the classic statistical definition of
variance as the contract terms may not subtract the mean. For example, suppose that
there are n+1 sample points S0,S1,...,Sn. Define, for i=1 to n, Ri = ln(Si / Si-1), the natural
log returns. Then
where A is an annualisation factor normally chosen to be approximately the number of
sampling points in a year (commonly 252). It can be seen that subtracting the mean
return will decrease the realised variance. If this is done, it is common to use n − 1 as
the divisor rather thann, corresponding to an unbiased estimate of the sample variance.
It is market practice to determine the number of contract units as follows:
where Nvol is the corresponding vega notional for a volatility swap.[1] This makes the
payoff of a variance swap comparable to that of avolatility swap, another less popular
instrument used to trade volatility.
Pricing and valuation
The variance swap may be hedged and hence priced using a portfolio of
European call and put options with weights inversely proportional to the square of strike.[2][3]
Any volatility smile model which prices vanilla options can therefore be used to price the
variance swap. For example, using the Heston model, a closed-form solution can be
derived for the fair variance swap rate. Care must be taken with the behaviour of the
smile model in the wings as this can have a disproportionate effect on the price.
We can derive the payoff of a variance swap using Ito's Lemma. We first assume that
the underlying stock is described as follows:
Applying Ito's formula, we get:
Taking integrals, the total variance is:
We can see that the total variance consists of a rebalanced hedge of and short a log
contract.
Using a static replication argument [4] , i.e., any twice continuously differentiable contract
can be replicated using a bond, a future and infinitely many puts and calls, we can show
that a short log contract position is equal to being short a futures contract and a
collection of puts and calls:
Taking expectations and setting the value of the variance swap equal to zero, we can
rearrange the formula to solve for the fair variance swap strike:
Where:
S0 is the initial price of the underlying security,
S * > 0 is an arbitrary cutoff,
K is the strike of the each option in the collection of options used.
Often the cutoff S * is chosen to be the current forward price S * = FT = S0erT, in which
case the fair variance swap strike can be written in the simpler form:
Uses
Many traders find variance swaps interesting or useful for their purity. An alternative
way of speculating on volatility is with an option, but if one only has interest in volatility
risk, this strategy will require constant delta hedging, so that direction risk of the
underlying security is approximately removed. What is more, a replicating portfolio of a
variance swap would require an entire strip of options, which would be very costly to
execute. Finally, one might often find the need to be regularly rolling this entire strip of
options so that it remains centered around the current price of the underlying security.
The advantage of variance swaps is that they provide pure exposure to the volatility of
the underlying price, as opposed to call and put options which may carry directional risk
(delta). The profit and loss from a variance swap depends directly on the difference
between realized and implied volatility.[5]
Another aspect that some speculators may find interesting is that the quoted strike is
determined by the implied volatility smile in the options market, whereas the ultimate
payout will be based upon actual realized variance. Historically, implied variance has
been above realized variance,[6] a phenomenon known as the Variance risk premium,
creating an opportunity for volatility arbitrage, in this case known as the rolling short
variance trade. For the same reason, these swaps can be used to hedge Options on
Realized Variance.
The features of a variance swap include:
the variance strike
the realised variance
the vega notional: Like other swaps, the payoff is determined based on
a notional amount that is never exchanged. However, in the case of a variance
swap, the notional amount is specified in terms of vega, to convert the payoff into
dollar terms.
The payoff of a variance swap is given as follows:
where:
Nvar = variance notional (a.k.a. variance units),
= annualised realised variance, and
= variance strike.[1]
The annualised realised variance is calculated based on a prespecified set of sampling
points over the period. It does not always coincide with the classic statistical definition of
variance as the contract terms may not subtract the mean. For example, suppose that
there are n+1 sample points S0,S1,...,Sn. Define, for i=1 to n, Ri = ln(Si / Si-1), the natural
log returns. Then
where A is an annualisation factor normally chosen to be approximately the number of
sampling points in a year (commonly 252). It can be seen that subtracting the mean
return will decrease the realised variance. If this is done, it is common to use n − 1 as
the divisor rather thann, corresponding to an unbiased estimate of the sample variance.
It is market practice to determine the number of contract units as follows:
where Nvol is the corresponding vega notional for a volatility swap.[1] This makes the
payoff of a variance swap comparable to that of avolatility swap, another less popular
instrument used to trade volatility.
Pricing and valuation
The variance swap may be hedged and hence priced using a portfolio of
European call and put options with weights inversely proportional to the square of strike.[2][3]
Any volatility smile model which prices vanilla options can therefore be used to price the
variance swap. For example, using the Heston model, a closed-form solution can be
derived for the fair variance swap rate. Care must be taken with the behaviour of the
smile model in the wings as this can have a disproportionate effect on the price.
We can derive the payoff of a variance swap using Ito's Lemma. We first assume that
the underlying stock is described as follows:
Applying Ito's formula, we get:
Taking integrals, the total variance is:
We can see that the total variance consists of a rebalanced hedge of and short a log
contract.
Using a static replication argument [4] , i.e., any twice continuously differentiable contract
can be replicated using a bond, a future and infinitely many puts and calls, we can show
that a short log contract position is equal to being short a futures contract and a
collection of puts and calls:
Taking expectations and setting the value of the variance swap equal to zero, we can
rearrange the formula to solve for the fair variance swap strike:
Where:
S0 is the initial price of the underlying security,
S * > 0 is an arbitrary cutoff,
K is the strike of the each option in the collection of options used.
Often the cutoff S * is chosen to be the current forward price S * = FT = S0erT, in which
case the fair variance swap strike can be written in the simpler form:
Uses
Many traders find variance swaps interesting or useful for their purity. An alternative
way of speculating on volatility is with an option, but if one only has interest in volatility
risk, this strategy will require constant delta hedging, so that direction risk of the
underlying security is approximately removed. What is more, a replicating portfolio of a
variance swap would require an entire strip of options, which would be very costly to
execute. Finally, one might often find the need to be regularly rolling this entire strip of
options so that it remains centered around the current price of the underlying security.
The advantage of variance swaps is that they provide pure exposure to thevolatility of
the underlying price, as opposed to call and put options which may carry directional risk
(delta). The profit and loss from a variance swap depends directly on the difference
between realized and implied volatility.[5]
Another aspect that some speculators may find interesting is that the quoted strike is
determined by the implied volatility smile in the options market, whereas the ultimate
payout will be based upon actual realized variance. Historically, implied variance has
been above realized variance,[6] a phenomenon known as the Variance risk premium,
creating an opportunity for volatility arbitrage, in this case known as the rolling short
variance trade. For the same reason, these swaps can be used to hedge Options on
Realized Variance.
What Does Swap Dealer Mean?
An individual who acts as the counterparty in a swap agreement for the fee (called a
spread. These are the market makers for the swap market. Because swap
arrangements aren't actively traded, swap dealers allow broker to standardize swap
contracts to some extent.
Equity Swap
A swap in which at least one party’s payments are based on the rate of return of an equity index, such as the S&P 500. The other party’s payments can be based on a fixed rate, a non-equity variable rate, or even a different equity index. Equity swaps provide an easy and inexpensive means of reallocating a portfolio to a different equity sector.
There are many ways to structure an equity swap. For example, the notional principal can be fixed or variable. A fixed notional principal would replicate the position of a portfolio that is rebalanced periodically to maintain the same dollar allocation to a particular asset class. A variable notional principal would reflect a portfolio that is not rebalanced, but whose allocations grow or recede due to changes in the relative market values of its asset classes. In addition, an equity swap can be set up so that one either absorbs or is hedged against the currency risk, depending upon the base currency used for the notational principal. Equity swaps can also be concentrated on specific industries, market sectors, or even individual stocks, though the latter is not common.
Equity swaps do have a potentially greater downside risk than interest rate swaps, since equity returns, unlike interest rates, can be negative. Thus, if one market used in an equity swap goes down while the other goes up, the responsibility for both sides of the payments could fall on just one of the parties.
Applications
Typically Equity Swaps are entered into in order to avoid transaction costs (including Tax), to avoid locally based dividend taxes, limitations on leverage (notably the US margin regime) or to get around rules governing the particular type of investment that an institution can hold.
Equity Swaps also provide the following benefits over plain vanilla equity investing:
1. An investor in a physical holding of shares loses possession on the shares once he sells his position. However, using an equity swap the investor can pass on the negative returns on equity position without losing the possession of the shares and hence voting rights. For example, let's say A holds 100 shares of a Petroleum Company. As the price of crude falls the investor believes the stock would start giving him negative returns in the short run. However, his holding gives him a strategic voting right in the board which he does not want to lose. Hence, he enters into an equity swap deal wherein he agrees to pay Party B the return on his shares against LIBOR+25bps on a notional amt. If A is proven right, he will get money from B on account of the negative return on the stock as well as LIBOR+25bps on the notional. Hence, he mitigates the negative returns on the stock without losing on voting rights.
2. It allows an investor to receive the return on a security which is listed in such a market where he cannot invest due to legal issues. For example, let's say A wants to invest in company X listed in Country C. However, A is not allowed to invest in Country C due to capital control regulations. He can however, enter into a contract with B, who is a resident of C, and ask him to buy the shares of company X and provide him with the return on share X and he agrees to pay him a fixed / floating rate of return.
Equity Swaps, if effectively used, can make investment barriers vanish and help an investor create leverage similar to those seen in derivative products.
Investment banks that offer this product usually take a riskless position by hedging the client's position with the underlying asset. For example, the client may trade a swap - say Vodafone. The
bank credits the client with 1,000 Vodafone at GBP1.45. The bank pays the return on this investment to the client, but also buys the stock in the same quantity for its own trading book (1,000 Vodafone at GBP1.45). Any equity-leg return paid to or due from the client is offset against realised profit or loss on its own investment in the underlying asset. The bank makes its money through commissions, interest spreads and dividend rake-off (paying the client less of the dividend than it receives itself). It may also use the hedge position stock (1,000 Vodafone in this example) as part of a funding transaction such as stock lending,repo or as collateral for a loan.
Fras:
n finance, a forward rate agreement (FRA) is a forward contract, an over-the-counter contract between parties that determines the rate of interest, or the currency exchange rate, to be paid or received on an obligation beginning at a future start date. The contract will determine the rates to be used along with the termination date and notional value.[1] On this type of agreement, it is only the differential that is paid on the notional amount of the contract. It is paid on the effective date. The reference rate is fixed one or two days before the effective date, dependent on the market convention for the particular currency. FRAs are over-the counter derivatives. A FRA differs from a swap in that a payment is only made once at maturity.
Many banks and large corporations will use FRAs to hedge future interest rate exposure. The buyer hedges against the risk of rising interest rates, while the seller hedges against the risk of falling interest rates. Other parties that use Forward Rate Agreements are speculators purely looking to make bets on future directional changes in interest rates.[citation needed]
In other words, a forward rate agreement (FRA) is a tailor-made, over-the-counter financial futures contract on short-term deposits. A FRA transaction is a contract between two parties to exchange payments on a deposit, called the Notional amount, to be determined on the basis of a short-term interest rate, referred to as the Reference rate, over a predetermined time period at a future date. FRA transactions are entered as a hedge against interest rate changes. The buyer of the contract locks in the interest rate in an effort to protect against an interest rate increase, while the seller protects against a possible interest rate decline. At maturity, no funds exchange hands; rather, the difference between the contracted interest rate and the market rate is exchanged. The buyer of the contract is paid if the reference rate is above the contracted rate, and the buyer pays to the seller if the reference rate is below the contracted rate. A company that seeks to hedge against a possible increase in interest rates would purchase FRAs, whereas a company that seeks an interest hedge against a possible decline of the rates would sell FRAs.
Payoff formula: The netted payment made at the effective date are as follows
The Fixed Rate is the rate at which the contract is agreed. The Reference Rate is typically Euribor or LIBOR.
α is the day count fraction, i.e. the portion of a year over which the rates are calculated, using the day count convention used in the money markets in the underlying currency. For EUR and USD this is generally the number of days divided by 360, for GBP it is the number of days divided by 365 days.
The Fixed Rate and Reference Rate are rates that should accrue over a period starting on the effective date, and then paid at the end of the period (termination date). However, as the payment is already known at the beginning of the period, it is also paid at the beginning. This is why the discount factor is used in the denominator.
FRAs Notation:
FRA Descriptive Notation and Interpretation
Notation Effective Date from now Termination Date from now Underlying Rate1 x 4 1 month 4 months 4-1 = 3 months LIBOR1 x 7 1 month 7 months 7-1 = 6 months LIBOR3 x 6 3 months 6 months 6-3 = 3 months LIBOR3 x 9 3 months 9 months 9-3 = 6 months LIBOR6 x 12 6 months 12 months 12-6 = 6 months LIBOR12 x 18 12 months 18 months 18-12 = 6 months LIBOR
How to interpret a quote for FRA?
[US$ 3x9 - 3.25/3.50%p.a ] - means deposit interest starting 3 months from now for 6 month is 3.25% and borrowing interest rate starting 3 months from now for 6 month is 3.50%.
It has been verified by Ananda Shailendra a CA (Final).
