options and speculative markets 2004-2005 introduction

Options and Speculative Markets2004-2005Introduction

Professor André Farber

Solvay Business School

Université Libre de Bruxelles

OMS 01 Introduction |2August 23, 2004

1.Introduction

• Outline of this session

1. Course outline

2. Derivatives

3. Forward contracts

4. Options contracts

5. The derivatives markets

6. Futures contracts


• Reference:

John HULL Options, Futures and Other Derivatives, Fifth edition, Prentice Hall 2003

• Copies of my slides will be available on my website: www.ulb.ac.be/cours/solvay/farber

• Grades:

– Cases: 20%

– Final exam: 80%


Course outline

Introduction

Pricing Forwards and Futures

Using Futures

IR Derivatives

Swaps

Case 1

Pricing Options

Inside Black Scholes

Using Options

IR Options 1

IR Options 2

Case 2


Derivatives

• A derivative is an instrument whose value depends on the value of other more basic underlying variables

• 2 main families:

• Forward, Futures, Swaps

• Options

• = DERIVATIVE INSTRUMENTS

• value depends on some underlying asset


Forward contract: Definition

• Contract whereby parties are committed:– to buy (sell)– an underlying asset– at some future date (maturity)– at a delivery price (forward price) set in advance

• The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)

• The forward price may be different for contracts of different maturities

• Buying forward = "LONG" position• Selling forward = "SHORT" position• When contract initiated: No cash flow• Obligation to transact


Forward contract: example

• Underlying asset: Gold

• Spot price: $380 / troy ounce

• Maturity: 6-month

• Size of contract: 100 troy ounces (2,835 grams)

• Forward price: $390 / troy ounce

Spot price 350 370 390 410 430

Buyer (long) -4,000 -2,000 0 +2,000 +4,000

Seller (short) +4,000 +2,000 0 -2,000 -4,000

Profit/Loss at maturity


Forward contract: Gains and losses

LONG SHORT

F FST

ST

Gain

Loss

0 0

Gain

Loss


Options contracts: Definition

• A call (put) contract gives to the owner

• - the right :

• - to buy (sell)

• - an underlying asset

• - on or before some future date (maturity)

• on : "European" option

• before: "American" option

• - at a price set in advance (the exercise price or striking price)

• Buyer pays a premium to the seller (writer)


Option contracts: example

• Underlying asset: Gold

• Spot price: $380 / troy ounce

• Maturity: 6-month

• Size of contract: 100 troy ounces (2,835 grams)

• Exercise price: $390 / troy ounce

• Premium Call $30 / troy ounce Put $34 / troy ounce

Spot price 350 370 390 410 430

Long call -3,000 -3,000 -3,000 -1,000 +1,000

Seller (short) +3,000 +3,000 +3,000 +1,000 -1,000

Long put +600 -1,400 -3,400 -3,400 -3,400

Short put -600 +1,400 +3,400 +3,400 +3,400


European call option: Terminal payoff

• Exercise option if, at maturity,

• ST > K

• then : CT = ST - K

• otherwise: CT = 0

• CT = MAX(0, ST - K)

Value at maturity

K S TStrikingprice

Stockprice


European call option: Profit at maturity

Profit at maturity

K S TStrikingprice

Stockprice

- Premium

Profit at maturity

K ST

Premium


European put option

• Exercise option if, at maturity, ST < K

• then PT = K - ST

• otherwise PT = 0

• PT = MAX(0, K - ST )

Value / profit at maturity

K S T

Strikingprice

Stockprice

Value

Profit

Premium


Put, call and forwards: put call parity

Long forwardLong call

Short put

Profit

STK

+ Call – Put = + Forward


Derivatives Markets

• Exchange traded

– Traditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic trading

– Contracts are standard there is virtually no credit risk

• Over-the-counter (OTC)

– A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managers

– Contracts can be non-standard and there is some small amount of credit risk


Global Market Size

Notional amount billions US$ Dec. 2002 Dec. 2003

OTC Derivatives 141,679 197,177

- Foreign exchanges contracts 18,460 24,484

- Interest rate contracts 121,799 141,991

- Equity-linked contracts 2,799 3,787

- Commodity contracts 923 1,040

-Other 21,952 25,510

Organized Exchanges 23,675 46,733

- IR Futures 9,956 13,123

- IR Options 11,759 20,793

- Currency Futures 47 80

- Currency Options 27 38

- Equity Index Futures 326 502

- Equity Index Options 1,700 2,197

Source: BIS Quarterly Review, June 2004 – www.bis.org


Evolution of global market

0

50,000

100,000

150,000

200,000

250,000

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Pri

nc

ipa

l A

mo

un

t U

SD

Bil

lio

ns

Markets OTC


Main Derivative markets

• EuropeEurex:http://www.eurexchange.com/

Liffe: http://www.liffe.com

Matif : http://www.matif.fr

• United StatesChicago Board of Tradehttp: //www.cbot.com


Why use derivatives?

• To hedge risks

• To speculate (take a view on the future direction of the market)

• To lock in an arbitrage profit

• To change the nature of a liability

• To change the nature of an investment without incurring the costs of selling one portfolio and buying another


Forward contract: Cash flows

• Notations

ST Price of underlying asset at maturity

Ft Forward price (delivery price) set at time t<T

Initiation Maturity T

Long 0 ST - Ft

Short 0 Ft - ST

• Initial cash flow = 0 :delivery price equals forward price.

• Credit risk during the whole life of forward contract.


Forward contract: Locking in the result before maturity

• Enter a new forward contract in opposite direction.

• Ex: at time t1 : long forward at forward price F1

• At time t2 (<T): short forward at new forward price F2

• Gain/loss at maturity :

• (ST - F1) + (F2 - ST ) = F2 - F1 no remaining uncertainty


Futures contract: Definition

• Institutionalized forward contract with daily settlement of gains and losses

• Forward contract

– Buy long sell short

• Standardized

– Maturity, Face value of contract

• Traded on an organized exchange

– Clearing house

• Daily settlement of gains and losses (Marked to market)


Example : Gold Futures (Comex – Nymex.com)

• Trading unit: 100 troy ounces (2,835 grams)

• July 3, 2002

Settle Open interest July 312.80 21 Aug 313.20 96,313 Oct 314.30 5,937 Dec 315.20 31,110 Fb03 316.00 7,566 June 317.70 5,457 Aug 318.70 4,014

Source: Wall Street Journal


Gold futures: contract specifications

•Trading MonthsFutures: Trading is conducted for delivery during the current calendar month, the next two calendar months, any February, April, August, and October thereafter falling within a 23-month period, and any June and December falling within a 60-month period beginning with the current month.Options: The nearest six of the following contract months: February, April, June, August, October, and December. Additional contract months - January, March, May, July, September, and November - will be listed for trading for a period of two months. A 24-month option is added on a June/December cycle.The options are American-style and can be exercised at any time up to expiration.On the first day of trading for any options contract month, there will be 13 strike prices each for puts and calls.

Price QuotationFutures and Options: Dollars and cents per troy ounce. For example: $301.70 per troy ounce.Minimum Price FluctuationFutures and Options: Price changes are registered in multiples of 10¢ ($0.10) per troy ounce, equivalent to $10 per contract. A fluctuation of $1 is, therefore, equivalent to $100 per contract.

Maximum Daily Price FluctuationFutures: Initial price limit, based upon the preceding day’s settlement price is $75 per ounce. Two minutes after either of the two most active months trades at the limit, trades in all months of futures and options will cease for a 15-minute period. Trading will also cease if either of the two active months is bid at the upper limit or offered at the lower limit for two minutes without trading.Trading will not cease if the limit is reached during the final 20 minutes of a day’s trading. If the limit is reached during the final half hour of trading, trading will resume no later than 10 minutes before the normal closing time.When trading resumes after a cessation of trading, the price limits will be expanded by increments of 100%. Options: No price limits.Last Trading DayFutures: Trading terminates at the close of business on the third to last business day of the maturing delivery month.Options: Expiration occurs on the second Friday of the month prior to the delivery month of the underlying futures contract.


Futures: Daily settlement and the clearing house

• In a forward contract:– Buyer and seller face each other during the life of the contract– Gains and losses are realized when the contract expires– Credit risk

BUYER SELLER• In a futures contract

– Gains and losses are realized daily (Marking to market)– The clearinghouse garantees contract performance : steps in to take a

position opposite each party

BUYER CH SELLER


Futures: Margin requirements

• INITIAL MARGIN : deposit to put up in a margin account by a person entering a futures contract

• MAINTENANCE MARGIN : minimum level of the margin account

• MARKING TO MARKET : balance in margin account adjusted daily

• Equivalent to writing a new futures contract every day at the new futures price

• (Remember how to close of position on a forward)

• Note: timing of cash flows different

+ Size x (Ft+1 -Ft) -Size x (Ft+1 -Ft)

LONG(buyer) SHORT(seller)


Example of a Futures Trade

• An investor takes a long position in 2 December gold futures contracts on June 5– contract size is 100 oz.

– futures price is US$400

– margin requirement is US$2,000/contract (US$4,000 in total)

– maintenance margin is US$1,500/contract (US$3,000 in total)


A Possible Outcome

Daily Cumulative Margin

Futures Gain Gain Account Margin

Price (Loss) (Loss) Balance Call

Day (US$) (US$) (US$) (US$) (US$)

400.00 4,000

5-Jun 397.00 (600) (600) 3,400 0. . . . . .. . . . . .. . . . . .

13-Jun 393.30 (420) (1,340) 2,660 1,340 . . . . . .. . . . .. . . . . .

19-Jun 387.00 (1,140) (2,600) 2,740 1,260 . . . . . .. . . . . .. . . . . .

26-Jun 392.30 260 (1,540) 5,060 0

+

= 4,000

3,000

+

= 4,000

<


Futures Contracts Example: Barings

• Long position on 20,000 Nikkei 225 Futures

• 1 index pt = Yen 1,000 = $ 10

• If Nikkei 225 = 20,000

• Size of contract = $ 200,000 position =$ 4,000 mio

• Date Nikkei 225• 30.12.9419,723• 25.02.9517,473 F = - 2,250

• Loss = F $/pt # contracts

• = (-2,250) ($ 10) (20,000) = $ 450,000,000

options and speculative markets 2004-2005 introduction

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