currency futures and options (chapter 7)

International Financial ManagementVicentiu Covrig

Currency Futures and Options(chapter 7)

The following sections in chapter 7 are not required for the exam:- American option-pricing relationships- European option-pricing relationships- Binomial option-pricing model- European option-pricing formula- Empirical tests of currency options

Futures Contracts: Preliminaries A futures contract is like a forward contract:

- It specifies that a certain currency will be exchanged for another at a specified time in the future at prices specified today.

A futures contract is different from a forward contract:- Futures are standardized contracts trading on

organized exchanges with daily resettlement through a clearinghouse

Futures Contracts: Preliminaries

Standardizing Features:- Contract Size- Delivery Month- Daily resettlement

Initial Margin (about 4% of contract value, cash or T-bills held in a street name at your brokers).

Daily Resettlement: An Example Consider a long position in the CME

Euro/U.S. Dollar contract. It is written on €125,000 and quoted in $ per €. The futures price is $1.30 per € the maturity is

3 months. At initiation of the contract, the long has in the

margin account $20,000.

Daily Resettlement: An ExampleThe futures price is $1.30 per € If tomorrow, the futures rate closes at $1.2 per €., then your

position’s value drops.Your original agreement was to buy €125,000 and pay125,000 x1.3=$162,500Now €125,000 is worth € 125,000 x1.2=$150,000

You have lost $12,500 = € 125,000 x (1.20-1.3)The $12,500 comes out of your $20,000 margin account

Daily Resettlement: An Example With futures contracts, we have daily

resettlement of gains and losses rather than one big settlement at maturity.

Every trading day:- If the price goes down, the long pays the short.- If the price goes up, the short pays the long.

After the daily resettlement, each party has a new contract at the new price with one-day-shorter maturity.

Toting Up At the end of his adventure, our investor has three ways of computing his gains and losses:1. Sum of daily gains and losses.– $7,500 = $1,250 – $1,250 – $3,750 – $1,250 – $2,500 2. Contract size times the difference between initial contract

price and last settlement price. – $7,500 = ($1.24/€ – $1.30/€) × €125,0003. Ending balance on the account minus beginning balance on

the account, adjusted for deposits or withdrawals. – $7,500 = $2,750 – ($6,500 + $3,750)

Forward vs. Futures Contracts

Basic differences:- Trading Locations- Contractual size- Settlement - Expiration date- Delivery

Interest Rate Parity Carefully Defined

No matter how you quote the exchange rate ($ per ¥ or ¥ per $) to find a forward rate, increase the dollars by the dollar rate and the foreign currency by the foreign currency rate:

1 + i$

1 + i¥F$/¥ = S$/¥ ×or1 + i$

1 + i¥F¥/$ = S¥/$ ×

Currency Futures Markets The CME Group (formerly Chicago Mercantile Exchange) is by

far the largest currency futures market. CME hours are 7:20 a.m. to 2:00 p.m. CST Monday-Friday. Extended-hours trading takes place Sunday through Thursday

(local) on GLOBEX i.e. from 5:00 p.m. to 4:00 p.m. CST the next day.

The Singapore Exchange offers interchangeable contracts. There are other markets, but none are close to CME and SIMEX

trading volume. Expiry cycle: March, June, September, December. The delivery date is the third Wednesday of delivery month. The last trading day is the second business day preceding the

delivery day.

Options Contracts: Preliminaries An option gives the holder the right, but not the

obligation, to buy or sell a given quantity of an asset in the future, at prices agreed upon today.

Calls vs. Puts- Call options gives the holder the right, but not the

obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today.

- Put options gives the holder the right, but not the obligation, to sell a given quantity of some asset at some time in the future, at prices agreed upon today.

Options Contracts: Preliminaries

The premium: the price of an option that the writer charges the buyer.

For currency options the strike price is the exchange rate at which the option holder can buy or sell the contracted currency

Options Contracts: Preliminaries Contract features:

- strike/exercise price- size of the contract- delivery month

European vs. American options- European options can only be exercised on the expiration date.- American options can be exercised at any time up to and

including the expiration date.- Since this option to exercise early generally has value,

American options are usually worth more than European options, other things equal.

Call Option

In-the-money- The exercise price is less than the spot price of the

underlying asset. At-the-money

- The exercise price is equal to the spot price of the underlying asset.

Out-of-the-money- The exercise price is more than the spot price of the

underlying asset.

Put Option

In-the-money- The exercise price is greater than the spot price of the

underlying asset. At-the-money

- The exercise price is equal to the spot price of the underlying asset.

Out-of-the-money- The exercise price is lower than the spot price of the

underlying asset.

Basic Option Pricing Relationships at Expiration

At expiration, an American call option is worth the same as a European option with the same characteristics.

If the call is in-the-money, it is worth ST – E. If the call is out-of-the-money, it is worthless.

CaT = CeT = Max[ST - E, 0] At expiry, an American put option is worth the same as a

European option with the same characteristics. If the put is in-the-money, it is worth E - ST. If the put is out-of-the-money, it is worthless.

PaT = PeT = Max[E - ST, 0]

EXAMPLE You buy a call on one € at $1, expiring on June

30th. You are long the call. The counter party is the writer of the call; he has

the potential obligation to deliver one Euro to you at $1 if you want him to (i.e. if you exercise the option)

If ST = $1.05 or $1.1, you will exercise your right and buy € at $1, and make 5 or 10¢, respectively.

If ST < $1you will not exercise.

Basic Option Profit Profiles

CaT = CeT = Max[ST - E, 0]

profit

E E+CST

Long 1 call

CaT = CeT = Max[ST - E, 0]profit

STshort 1 call

PaT = PeT = Max[E - ST, 0]

profit

E - pST

long 1 put

PaT = PeT = Max[E-ST , 0]

profit

Short 1 putE - p

Option premium

Intrinsic Value- The difference between the exercise price of the option

and the spot price of the underlying asset or zero. Speculative Value

- The difference between the option premium and the intrinsic value of the option.

Option Premium

= Intrinsic Value

+ Speculative Value

The determinants of time value of option prices

a. value rises with longer time to expiration.

b. value rises when greater volatility in the exchange rate.

c. Value is complicated by both the home and foreign interest

rates.

ExampleFor a call on Euro with strike price k = US¢/€ 91.5. The intrinsic value is 5¢ if the spot rate is 96.5¢. Time value is 1¢ if the market price is 6¢. The intrinsic value is 0 if the spot rate is 88¢ (or any other

price equal to or below 91.5¢). Time value is 2¢ if market price is 2.

For put with strike price k = US¢/€ 91.5. The intrinsic value is 0 if the spot rate is 96.5¢. Time value is 2 if the market price is 2¢. The intrinsic value is 3.5¢ if the spot rate is 88¢. Time

value is 1.5¢ if market price is 5.

The call premium per British pound on February 1 is $0.011; the expiration date is June, and the strike price is $1.6. You anticipates that the spot rate will increase to $1.7 by May1. If your expectation proves correct, what should be your dollar profit from speculating one pound call option (31,250 units per contract)?

Buy one call option on February 1 -$0.011 per poundExercise the option on May 1 -$1.60 per poundSell the pound on May 1 +$1.70 per poundNet profit per pound +$0.089

Net profit per contract: £31,250x $0.089=$2,781.25

Example

Black–Scholes Pricing Formulae

The Black-Scholes formulae for the price of a European call and a put written on currency are:

)N()N( 210$ dEedeSc TrTri

Tdd 12

N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d.

TrT edFdEp $)]N()N([ 12

Learning outcomes• Discuss the similarities and differences between forward and futures.• Define the call and put options; the obligations or/and options of the buyers and sellers• Explain the differences between European and American options• Know the basic option pricing relationships at expiration• Basic option profit profiles (all four of them)• Know how to calculate the intrinsic value and time value of the options• Know how to calculate the profit/loss of long/short call and put speculative

positions (for example, see the numerical examples done in class)•

currency futures and options (chapter 7)

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