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Currency Futures and Options (chapter 7)

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

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Currency Futures and Options (chapter 7)

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  1. Currency Futures and Options (chapter 7)

  2. 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

  3. 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

  4. 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).

  5. 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.

  6. Daily Resettlement: An Example The 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 pay 125,000 x1.3=$162,500 Now €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

  7. 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.

  8. Toting Up • At the end of his adventure, our investor has three ways of computing his gains and losses: • Sum of daily gains and losses. – $7,500 = $1,250 – $1,250 – $3,750 – $1,250 – $2,500 • Contract size times the difference between initial contract price and last settlement price. – $7,500 = ($1.24/€– $1.30/€) × €125,000 • Ending balance on the account minus beginning balance on the account, adjusted for deposits or withdrawals. – $7,500 = $2,750 – ($6,500 + $3,750)

  9. Forward vs. Futures Contracts Basic differences: - Trading Locations - Contractual size - Settlement - Expiration date - Delivery

  10. 1 + i$ F$/¥ = S$/¥ × 1 + i¥ 1 + i¥ or F¥/$= S¥/$× 1 + i$ 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:

  11. 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.

  12. 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.

  13. 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.

  14. Options Contracts: Preliminaries • 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.

  15. 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

  16. 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]

  17. 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.

  18. Basic Option Profit Profiles CaT = CeT = Max[ST - E, 0] profit Long 1 call ST -C E+C E loss

  19. Basic Option Profit Profiles CaT = CeT = Max[ST - E, 0] profit C ST E E+C short 1 call loss

  20. Basic Option Profit Profiles PaT = PeT = Max[E - ST, 0] profit long 1 put ST E - p -p E loss

  21. Basic Option Profit Profiles PaT = PeT = Max[E-ST, 0] profit p ST Short 1 put E - p E loss

  22. Option premium • Intrinsic Value • The difference between the exercise price of the option and the spot price of the underlying asset. • Speculative Value • The difference between the option premium and the intrinsic value of the option. Option Premium Intrinsic Value Speculative Value = +

  23. 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.

  24. Example For 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.

  25. Example 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 pound Exercise the option on May 1 -$1.60 per pound Sell the pound on May 1 +$1.70 per pound Net profit per pound +$0.089 Net profit per contract: £31,250x $0.089=$2,781.25

  26. Black–Scholes Pricing Formulae The Black-Scholes formulae for the price of a European call and a put written on currency are: N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d.

  27. 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)

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