chapter 7 The following sections in chapter 7 are not required for the exam American optionpricing relationships European optionpricing relationships Binomial optionpricing model ID: 1028645
Download Presentation The PPT/PDF document "Currency Futures and Options" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
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: PreliminariesA 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: PreliminariesStandardizing Features:Contract SizeDelivery MonthDaily resettlementInitial Margin (about 4% of contract value, cash or T-bills held in a street name at your brokers).
5. Daily Resettlement: An ExampleConsider 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 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=$150,000You 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 ExampleWith 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/€) × €125,000Ending balance on the account minus beginning balance on the account, adjusted for deposits or withdrawals. – $7,500 = $2,750 – ($6,500 + $3,750)
9. Forward vs. Futures Contracts Basic differences: - Trading Locations - Contractual size - Settlement - Expiration date - Delivery
10. Interest Rate Parity Carefully DefinedNo matter how you quote the exchange rate ($ 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¥/$ ×
11. Currency Futures MarketsThe 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: PreliminariesAn 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. PutsCall 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: PreliminariesThe 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
14. Options Contracts: PreliminariesContract features: - strike/exercise price - size of the contract - delivery monthEuropean vs. American optionsEuropean 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.
15. Call OptionIn-the-moneyThe exercise price is less than the spot price of the underlying asset.At-the-moneyThe exercise price is equal to the spot price of the underlying asset.Out-of-the-moneyThe exercise price is more than the spot price of the underlying asset.
16. Put OptionIn-the-moneyThe exercise price is greater than the spot price of the underlying asset.At-the-moneyThe exercise price is equal to the spot price of the underlying asset.Out-of-the-moneyThe exercise price is lower than the spot price of the underlying asset.
17. Basic Option Pricing Relationships at ExpirationAt 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]
18. EXAMPLEYou 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.
19. Basic Option Profit ProfilesCaT = CeT = Max[ST - E, 0]profitlossEE+CSTLong 1 call-C
20. Basic Option Profit ProfilesCaT = CeT = Max[ST - E, 0]profitlossEE+CSTshort 1 callC
21. Basic Option Profit ProfilesPaT = PeT = Max[E - ST, 0]profitlossEE - pSTlong 1 put-p
22. Basic Option Profit ProfilesPaT = PeT = Max[E-ST , 0]profitlossESTShort 1 putE - pp
23. Option premiumIntrinsic ValueThe difference between the exercise price of the option and the spot price of the underlying asset or zero.Speculative ValueThe difference between the option premium and the intrinsic value of the option.Option Premium=Intrinsic Value+Speculative Value
24. 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.
25. 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.
26. 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 +$0.089Net profit per contract: £31,250x $0.089=$2,781.25Example
27. Black–Scholes Pricing FormulaeThe 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.
28. 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)