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Chapter Objective: This chapter discusses exchange-traded currency futures contracts, options contracts, and options on

Futures and Options on Foreign Exchange. 7. Chapter Seven. Chapter Objective: This chapter discusses exchange-traded currency futures contracts, options contracts, and options on currency futures. 7- 0. Chapter Outline. Futures Contracts: Preliminaries Currency Futures Markets

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Chapter Objective: This chapter discusses exchange-traded currency futures contracts, options contracts, and options on

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  1. Futures and Options on Foreign Exchange 7 Chapter Seven Chapter Objective: This chapter discusses exchange-traded currency futures contracts, options contracts, and options on currency futures. 7-0

  2. Chapter Outline • Futures Contracts: Preliminaries • Currency Futures Markets • Basic Currency Futures Relationships • Eurodollar Interest Rate Futures Contracts • Options Contracts: Preliminaries • Currency Options Markets • Currency Futures Options 7-1

  3. Chapter Outline (continued) • Basic Option Pricing Relationships at Expiry • American Option Pricing Relationships • European Option Pricing Relationships • Binomial Option Pricing Model • European Option Pricing Model • Empirical Tests of Currency Option Models 7-2

  4. 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. 7-3

  5. Futures Contracts: Preliminaries • Standardizing Features: • Contract Size • Delivery Month • Daily resettlement • Initial performance bond (about 2 percent of contract value, cash or T-bills held in a street name at your brokerage). 7-4

  6. 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 strike price is $1.30; the maturity is 3 months. • At initiation of the contract, the long posts an initial performance bond of $6,500. • The maintenance performance bond is $4,000. 7-5

  7. Daily Resettlement: An Example • Recall that an investor with a long position gains from increases in the price of the underlying asset. • Our investor has agreed to BUY €125,000 at $1.30 per euro in three months time. • With a forward contract, at the end of three months, if the euro was worth $1.24, he would lose $7,500 = ($1.24 – $1.30) × 125,000. • If instead at maturity the euro was worth $1.35, the counterparty to his forward contract would pay him $6,250 = ($1.35 – $1.30) × 125,000. 7-6

  8. Daily Resettlement: An Example • With futures, we have daily resettlement of gains an 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. 7-7

  9. Performance Bond Money • Each day’s losses are subtracted from the investor’s account. • Each day’s gains are added to the account. • In this example, at initiation the long posts an initial performance bond of $6,500. • The maintenance level is $4,000. • If this investor loses more than $2,500 he has a decision to make: he can maintain his long position only by adding more funds—if he fails to do so, his position will be closed out with an offsetting short position. 7-8

  10. Daily Resettlement: An Example • Over the first 3 days, the euro strengthens then depreciates in dollar terms: Settle Gain/Loss Account Balance $1.31 $1,250 = ($1.31 – $1.30)×125,000 $7,750 = $6,500 + $1,250 $1.30 –$1,250 $6,500 + $3,750 = $6,500 $1.27 –$3,750 $2,750 On third day suppose our investor keeps his long position open by posting an additional $3,750. 7-9

  11. Daily Resettlement: An Example • Over the next 2 days, the long keeps losing money and closes out his position at the end of day five. Settle Gain/Loss Account Balance $1.31 $1,250 $7,750 $1.30 –$1,250 $6,500 $1.27 –$3,750 $2,750 + $3,750 = $6,500 = $6,500 – $1,250 $1.26 –$1,250 $5,250 $1.24 –$2,500 $2,750 7-10

  12. Toting Up • At the end of his adventures, 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 account minus beginning balance on account, adjusted for deposits or withdrawals. – $7,500 = $2,750 – ($6,500 + $3,750) 7-11

  13. Daily Resettlement: An Example Settle Gain/Loss Account Balance Total loss = – $7,500 $1.30 –$– $6,500 $1.31 $1,250 $7,750 $1.30 –$1,250 $6,500 $1.27 –$3,750 $2,750 + $3,750 $1.26 –$1,250 $5,250 $1.24 –$2,500 $2,750 = ($1.24 – $1.30) × 125,000 = $2,750 – ($6,500 + $3,750) 7-12

  14. Currency Futures Markets • The Chicago Mercantile Exchange (CME) is by far the largest. • Others include: • The Philadelphia Board of Trade (PBOT) • The MidAmerica Commodities Exchange • The Tokyo International Financial Futures Exchange • The London International Financial Futures Exchange 7-13

  15. The Chicago Mercantile Exchange • Expiry cycle: March, June, September, December. • Delivery date third Wednesday of delivery month. • Last trading day is the second business day preceding the delivery day. • CME hours 7:20 a.m. to 2:00 p.m. CST. 7-14

  16. CME After Hours • Extended-hours trading on GLOBEX runs from 2:30 p.m. to 4:00 p.m dinner break and then back at it from 6:00 p.m. to 6:00 a.m. CST. • The Singapore Exchange offers interchangeable contracts. • There are other markets, but none are close to CME and SIMEX trading volume. 7-15

  17. Reading Currency Futures Quotes OPEN INT OPEN HIGH LOW SETTLE CHG Euro/US Dollar (CME)—€125,000; $ per € Mar 1.4748 1.4830 1.4700 1.4777 .0028 172,396 Jun 1.4737 1.4818 1.4693 1.4763 .0025 2,266 Closing price Expiry month Daily Change Opening price Lowest price that day Number of open contracts Highest price that day 7-16

  18. Basic Currency Futures Relationships • Open Interest refers to the number of contracts outstanding for a particular delivery month. • Open interest is a good proxy for demand for a contract. • Some refer to open interest as the depth of the market. The breadth of the market would be how many different contracts (expiry month, currency) are outstanding. 7-17

  19. OPEN INT OPEN HIGH LOW SETTLE CHG Euro/US Dollar (CME)—€125,000; $ per € Mar 1.4748 1.4830 1.4700 1.4777 .0028 172,396 Jun 1.4737 1.4818 1.4693 1.4763 .0025 2,266 Reading Currency Futures Quotes Notice that open interest is greatest in the nearby contract, in this case March, 2008. In general, open interest typically decreases with term to maturity of most futures contracts. 7-18

  20. OPEN INT OPEN HIGH LOW SETTLE CHG Euro/US Dollar (CME)—€125,000; $ per € Mar 1.4748 1.4830 1.4700 1.4777 .0028 172,396 Jun 1.4737 1.4818 1.4693 1.4763 .0025 2,266 Basic Currency Futures Relationships The holder of a long position is committing himself to pay $1.4777 per euro for €125,000—a $184,712.50 position. As there are 172,396 such contracts outstanding, this represents a notational principal of over $31.8 billion! 7-19

  21. OPEN INT OPEN HIGH LOW SETTLE CHG Euro/US Dollar (CME)—€125,000; $ per € Mar 1.4748 1.4830 1.4700 1.4777 .0028 172,396 Jun 1.4737 1.4818 1.4693 1.4763 .0025 2,266 1 + i$ F($/€) = 1 + i€ S($/€) Reading Currency Futures Quotes Recall from chapter 6, our interest rate parity condition: 7-20

  22. OPEN INT OPEN HIGH LOW SETTLE CHG Euro/US Dollar (CME)—€125,000; $ per € Mar 1.4748 1.4830 1.4700 1.4777 .0028 172,396 Jun 1.4737 1.4818 1.4693 1.4763 .0025 2,266 Reading Currency Futures Quotes From March to June 2008 we should expect lower interest rates in dollar denominated accounts: if we find a higher rate in a euro denominated account, we may have found an arbitrage. 7-21

  23. 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. 7-22

  24. Options Contracts: Preliminaries • 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. 7-23

  25. 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. 7-24

  26. Options Contracts: Preliminaries • 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 + = 7-25

  27. Currency Options Markets • PHLX • HKFE • 20-hour trading day. • OTC volume is much bigger than exchange volume. • Trading is in six major currencies against the U.S. dollar. 7-26

  28. PHLX Currency Option Specifications http://www.phlx.com/products/xdc_specs.htm 7-27

  29. Basic Option Pricing Relationships at Expiry • At expiry, 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] 7-28

  30. Basic Option Pricing Relationships at Expiry • 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] 7-29

  31. Out-of-the-money In-the-money Basic Option Profit Profiles Profit Owner of the call If the call is in-the-money, it is worth ST – E. If the call is out-of-the-money, it is worthless and the buyer of the call loses his entire investment of c0. Long 1 call ST –c0 E + c0 E loss 7-30

  32. E + c0 Out-of-the-money In-the-money E Basic Option Profit Profiles Profit Seller of the call If the call is in-the-money, the writer loses ST – E. If the call is out-of-the-money, the writer keeps the option premium. c0 ST short 1 call loss 7-31

  33. E – p0 In-the-money Out-of-the-money E Basic Option Profit Profiles Profit Owner of the put If the put is in-the-money, it is worth E– ST. The maximum gain is E – p0 If the put is out-of-the-money, it is worthless and the buyer of the put loses his entire investment of p0. E – p0 ST – p0 long 1 put loss 7-32

  34. E – p0 E Basic Option Profit Profiles Profit Seller of the put If the put is in-the-money, it is worth E–ST. The maximum loss is – E + p0 If the put is out-of-the-money, it is worthless and the seller of the put keeps the option premium of p0. p0 ST short 1 put – E + p0 loss 7-33

  35. $1.75 Example Profit • Consider a call option on €31,250. • The option premium is $0.25 per € • The exercise price is $1.50 per €. Long 1 call on 1 pound ST –$0.25 $1.50 loss 7-34

  36. $1.75 Example Profit • Consider a call option on €31,250. • The option premium is $0.25 per € • The exercise price is $1.50 per €. Long 1 call on €31,250 ST –$7,812.50 $1.50 loss 7-35

  37. –$4,687.50 $1.35 Example Profit What is the maximum gain on this put option? At what exchange rate do you break even? $42,187.50 = €31,250×($1.50 – $0.15)/€ $42,187.50 • Consider a put option on €31,250. • The option premium is $0.15 per € • The exercise price is $1.50 per euro. ST Long 1 put on €31,250 $1.50 $4,687.50 = €31,250×($0.15)/€ loss 7-36

  38. American Option Pricing Relationships • With an American option, you can do everything that you can do with a European option AND you can exercise prior to expiry—this option to exercise early has value, thus: CaT>CeT = Max[ST - E, 0] PaT>PeT = Max[E - ST, 0] 7-37

  39. Out-of-the-money In-the-money Market Value, Time Value and Intrinsic Value for an American Call Profit The red line shows the payoff at maturity, not profit, of a call option. Note that even an out-of-the-money option has value—time value. Long 1 call Market Value Intrinsic value ST Time value loss E 7-38

  40. ST E (1 + i$) (1 + i£) The cash flow today is – The cash flow today is European Option Pricing Relationships Consider two investments • Buy a European call option on the British pound futures contract. The cash flow today is –Ce • Replicate the upside payoff of the call by • Borrowing the present value of the dollar exercise price of the call in the U.S. at i$ • Lending the present value of ST at i£ 7-39

  41. ST E – , 0 Ce>Max (1 + i£) (1 + i$) European Option Pricing Relationships When the option is in-the-money both strategies have the same payoff. When the option is out-of-the-money it has a higher payoff than the borrowing and lending strategy. Thus: 7-40

  42. E ST – , 0 Pe>Max (1 + i$) (1 + i£) European Option Pricing Relationships Using a similar portfolio to replicate the upside potential of a put, we can show that: 7-41

  43. 0 1 $1.5147 F1($/€) = €1.00 A Brief Review of IRP Recall that if the spot exchange rate is S0($/€) = $1.50/€, and that if i$ = 3% and i€ = 2% then there is only one possible 1-year forward exchange rate that can exist without attracting arbitrage: F1($/€) = $1.5147/€ • Borrow $1.5m at i$ = 3% • Owe $1.545m • Exchange $1.5m for €1m at spot • Invest €1m at i€ = 2% • Receive €1.02 m 7-42

  44. Binomial Option Pricing Model Imagine a simple world where the dollar-euro exchange rate is S0($/€) = $1.50/€ today and in the next year, S1($/€) is either $1.875/€ or $1.20/€. S0($/€) S1($/€) $1.875 $1.50 $1.20 7-43

  45. S0($/€) C1($/€) S1($/€) $1.875 $.375 $1.50 …and if S1($/€) = $1.20/€ the option is out-of-the-money: $1.20 $0 Binomial Option Pricing Model A call option on the euro with exercise priceS0($/€) = $1.50 will have the following payoffs. By exercising the call option, you can buy €1 for $1.50. If S1($/€) = $1.875/€ the option is in-the-money: 7-44

  46. S0($/€) C1($/€) S1($/€) $1.875 $.375 $1.50 $1.20 $0 Binomial Option Pricing Model We can replicate the payoffs of the call option. By taking a position in the euro along with some judicious borrowing and lending. 7-45

  47. Binomial Option Pricing Model Borrow the present value (discounted at i$) of $1.20 today and use that to buy the present value (discounted at i€) of €1. Invest the euro today and receive €1 in one period. Your net payoff in one period is either $0.675 or $0. S0($/€) debt portfolio C1($/€) S1($/€) $1.875 – $1.20 = $.675 $.375 $1.50 $1.20 $0 – $1.20 = $0 7-46

  48. $.675 1.80 = $.375 S0($/€) debt portfolio C1($/€) S1($/€) $1.875 – $1.20 = $.675 $.375 $1.50 $1.20 $0 – $1.20 = $0 Binomial Option Pricing Model The portfolio has 1.8 times the call option’s payoff so the portfolio is worth 1.8 times the option value. 7-47

  49. $1.20 €1.00 $1.50 × – (1 + i€) €1.00 (1 + i$) S0($/€) debt portfolio C1($/€) S1($/€) $1.875 – $1.20 = $.675 $.375 $1.50 $1.20 $0 – $1.20 = $0 Binomial Option Pricing Model The replicating portfolio’s dollar value today is the sum of today’s dollar value of the present value of one euro less the present value of a $1.20 debt: 7-48

  50. $1.20 €1.00 $1.50 5 × – × (1 + i€) €1.00 C0 = (1 + i$) 9 If i$ = 3% and i€ = 2% the call is worth 5 $1.20 €1.00 $1.50 × $0.1697 = – × (1.03) 9 (1.02) €1.00 Binomial Option Pricing Model We can value the call option as 5/9 of the value of the replicating portfolio: S0($/€) debt portfolio C1($/€) S1($/€) $1.875 – $1.20 = $.675 $.375 $1.50 $1.20 $0 – $1.20 = $0 7-49

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