INTERNATIONAL FINANCIAL MANAGEMENT

Chapter Nine 9 Futures and Options on Foreign Exchange INTERNATIONAL FINANCIAL MANAGEMENT Chapter Objective: This chapter discusses exchange-traded currency futures contracts, options contracts, and options on currency futures. EUN / RESNICK Second Edition

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

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

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 • Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically you think that the dollar will appreciate). Currently $1 = ¥140. The 3-month forward price is $1=¥150.

Daily Resettlement: An Example • Currently $1 = ¥140 and it appears that the dollar is strengthening. • If you enter into a 3-month futures contract to sell ¥ at the rate of $1 = ¥150 you will make money if the yen depreciates. The contract size is ¥12,500,000 • Your initial margin is 4% of the contract value:

Daily Resettlement: An Example If tomorrow, the futures rate closes at $1 = ¥149, then your position’s value drops. Your original agreement was to sell ¥12,500,000 and receive $83,333.33 But now ¥12,500,000 is worth $83,892.62 You have lost $559.28 overnight.

Daily Resettlement: An Example • The $559.28 comes out of your $3,333.33 margin account, leaving $2,774.05 • This is short of the $3,355.70 required for a new position. • Your broker will let you slide until you run through your maintenance margin. Then you must post additional funds or your position will be closed out. This is usually done with a reversing trade.

Daily Resettlement: Short Position * • Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically you think that the dollar will appreciate). Currently $1 = ¥140. The 3-month forward price is $1=¥150.

Daily Resettlement: An Example * Daily Resettlement: Short Position * • What do we have ? • Spot rate for yen:$1= ¥140 (or, ¥1=$1/140) • 3-month futures contract (¥12,500,000 each contract) quotes at:$1= ¥150 (or, ¥1=$1/150) • If you expect that dollar will appreciate (that is, yen will depreciate), and wish to make profit from futures speculation, what will you do?

Daily Resettlement: Short Position * Daily Resettlement: An Example * • You will sell¥ at the rate of$1= ¥150 today. This means that you agree to sell ¥12,500,000 and receive $83,333.33=¥12,500,000×($1/ ¥150) three months later. • You deposit your initial margin (4% of the contract value=$83,333.33×0.04=$3,333.33) to meet you margin requirement. • On the next day, the futures rate closes at $1=¥149 (¥ appreciates), what happens to your investment? • This means that if you want to close your position, you shall buy ¥ at $1=¥ 149. That is, you should pay $83,892.62=¥ 12,500,000×($1/¥ 149).

Daily Resettlement: Short Position * Daily Resettlement: An Example * • Your profit will be $83,333.33-$83,892.62= -$559.28 if you close your position today. • This means that your “opportunity cost” is $559.28 if you do not really close your position. (Or, think it in another way, those who sell ¥ futures today can receive $83,892.62 while you can only receive $83,333.33) • This loss in value is than reflected in your margin account, with its new balance $2,774.05=$3,333.33-$559.28. • On the next day, if the settlement price is $1=¥ 146, and assume that the maintenance margin is $2,500, what happens then?

Daily Resettlement: Short Position * Daily Resettlement: An Example * • Your profit will be ¥12,500,000×[($1/¥149)-($1/¥146)]=-1,723.82(note that by daily resettlement, your contract rate is renewed to $1=¥149 yesterday, not $1=¥150!) • Again, this loss in value will be reflected in your margin account, with its new balance $1,050.23=$2,774.05-$1,723.82.(This also equals to 3,333.33+12,500,000[(1/150)-(1/146)].) • Now, your margin account has its balance lower than the maintenance margin ($2,500). You should deposit money into your account until it meets the margin requirement which is now ¥12,500,000×($1/¥146) ×0.04=$3424.66.(You have to deposit $3,424.66-$1,723.82=$1,700.84 into your account.)

Daily Resettlement: Long Position * What happens if you expect that ¥ will appreciate? * • Other things being equal, how will you speculate using futures contract if you expect that ¥ will be appreciating, instead of depreciating? • You will buy¥ at the rate of$1= ¥150 today. This means that you agree to pay $83,333.33=¥12,500,000×($1/ ¥150) to buy ¥12,500,000 three months later. • You deposit your initial margin (4% of the contract value=$83,333.33×0.04=$3,333.33) to meet you margin requirement. • On the next day, the futures rate closes at $1=¥149 (¥ appreciates, as you expected), what happens to your investment? • This means that if you want to close your position, you shall sell ¥ at $1=¥ 149. That is, you will receive $83,892.62=¥ 12,500,000×($1/¥ 149).

Daily Resettlement: Long Position * What happens if you expect that ¥ will appreciate? * • Your profit will be $83,892.62-$83,333.33= $559.28 if you close your position today. • This means that your “opportunity profit” is $559.28 if you do not really close your position. (Or, think it in another way, those who buy ¥ futures today should pay $83,892.62 while you only have to pay $83,333.33) • This gain in value is than reflected in your margin account, with its new balance $3,892.61=$3,333.33+$559.28. • On the next day, if the settlement price is $1=¥146, and assume that the maintenance margin is $2,500, what happens then?

Daily Resettlement: Long Position * What happens if you expect that ¥ will appreciate? * • Your profit will be ¥12,500,000×[($1/¥146)-($1/¥149)]= $1,723.82(Again, by daily resettlement, your contract rate is renewed to $1=¥149 yesterday, not $1=¥150!) • This gain in value will be reflected into your margin account, with its new balance $5,616.43= $3,892.61 +$1,723.82.(This also equals to 3,333.33+12,500,000[(1/146)-(1/150)].) • Now, your margin account balance is still greater than the maintenance margin. You do not have to do anything to your margin account. Or, you can withdraw your profit as long as your margin account balance is still greater than its maintenance margin.

What do we learn from this example? * • Comparing the gain or loss made by both cases, you will learn that as the textbook stated, futures trading between the long and the short is a zero-sum game. That is, the gain of the long is exactly the loss of the short, and vice versa.

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

The Chicago Mercantile Exchange • Expiry cycle: March, June, September, December. • Delivery date 3rd 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.

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. • Singapore International Monetary Exchange (SIMEX) offer interchangeable contracts. • There’s other markets, but none are close to CME and SIMEX trading volume.

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.

Reading a Futures Quote Highest and lowest prices over the lifetime of the contract. Daily Change Closing price Lowest price that day Highest price that day Opening price Number of open contracts Expiry month

Eurodollar Interest Rate Futures Contracts • Widely used futures contract for hedging short-term U.S. dollar interest rate risk. • The underlying asset is a hypothetical $1,000,000 90-day Eurodollar deposit—the contract is cash settled. • Traded on the CME and the Singapore International Monetary Exchange. • The contract trades in the March, June, September and December cycle.

EURODOLLAR (CME)—$1 million; pts of 100% Open High Low Settle Chg Yield Settle Change Open Interest July 94.69 94.69 94.68 94.68 -.01 5.32 +.01 47,417 Reading Eurodollar Futures Quotes Eurodollar futures prices are stated as an index number of three-month LIBOR calculated as F = 100-LIBOR. The closing price for the July contract is 94.68 thus the implied yield is 5.32 percent = 100 – 94.68 The change was .01 percent of $1 million representing $100 on an annual basis. Since it is a 3-month contract one basis point corresponds to a $25 price change.

Daily Resettlements: Long Position* • Suppose that, the July contract closes at 94.50 today. Thus, the implied yield is 5.50% (=100-94.5). This means that if you buy (long) one 90-day Eurodollar interest rate futures (contract size=$1 million), you are guaranteed to receive $13,750= $1,000,000×5.5%×(90/360) on your July investment. • On the next day, the July contract closes at 94.51 (one basis point more than yesterday), what happens to your margin account? • The implied yield now is 5.49% (100-94.51). This means that the buyer of the contract is guaranteed to receive $13,725= $1,000,000×5.49%×(90/36) on the same July investment. • You earn $25=$13,750-$13,725 more than the new investor. This “opportunity profit” (because you are guaranteed with higher interest rate) will be added into your margin account.

Daily Resettlements: Long Position* • Your profit is calculated by [5.5%-5.49%] ×$1,000,000×(90/360)=$25. • Note that this is can also be calculated by [(100-94.50)-(100-94.51)] ×1%×$1,000,000×(90/360).That is , your profit can also be calculated by[94.51-94.5] ×1%×$1,000,000×(90/360)=$25, as the usual formula calculating futures contracts’ payoff. • Then you can see why the interest rate futures contracts are quoted this way. • Note also that from this example, you shall see why one basis point change in quotation corresponds to a $25 price change.

Daily Resettlements: Short Position* • Suppose that, the July contract closes at 94.50 today. Thus, the implied yield is 5.50% (=100-94.5). This means that if you sell (short) one 90-day Eurodollar interest rate futures (contract size=$1 million), you are guaranteed that you will have to pay $13,750= $1,000,000×5.5%×(90/360) on your July borrowing. • On the next day, the July contract closes at 94.51 (one basis point more than yesterday), what happens to your margin account? • The implied yield now is 5.49% (100-94.51). This means that the seller of the contract is guaranteed with interest cost of $13,725= $1,000,000×5.49%×(90/36) on the same July borrowing. • Youloss $25=$13,750-$13,725 because you have to pay more interest payment on the same borrowing. This “opportunity cost” will be deducted from your margin account.

Daily Resettlements: Short Position* • Your profit is calculated by [5.49%-5.5%] ×$1,000,000×(90/360)= -$25. • Note that this is can also be calculated by [(100-94.51)-(100-94.50)] ×1%×$1,000,000×(90/360).That is , your profit can also be calculated by[94.50-94.51] ×1%×$1,000,000×(90/360)= -$25, as the usual formula calculating futures contracts’ payoff. • Now, it’s your term to think which position you will take if you expect that the 90-day LIBOR will be rising, and wish to speculate from interest rate futures. • Also, think what if you expect that the 90-day LIBOR is declining?

Eurodollar Futures Hedge if You are an Investor * • You are a treasurer of a MNC, and expect to receive $2,000,000 on Sept. 17, 2003, because of your merchandise sale. You wish to invest these $2,000,000 in Eurodollar deposit because you know that the money will not be needed for a period of 90 days. • Today, the settlement price of the Sept03 interest rate futures is 94.00. • If you are uncertain about what interest rate you are going to receive, and wish to lock the return of your investment. How will you hedge against this interest rate risk? (You are worrying that the prevailing interest rate on that day will be very low.)

Eurodollar Futures Hedge if You are an Investor * • You will buy (long) 2 Euro dollar interest rate futures contracts at 94.00. This means that you can lock your return from investment at 6% p.a. (that is, you lock your return from 90-day euro dollar deposit at $2,000,000×6%×(90/360)=$30,000.) • We will demonstrate that no matter what the realized interest rate at Sept. 17 2003 is, your return is not altered since you’ve hedged your interest rate risk.

Eurodollar Futures Hedge if You are an Investor * 1. What happens if the 3-month LIBOR is 5% p.a. on Sept. 2003?a. You deposit your $2,000,000 at that realized interest rate 5% p.a., which gives you $2,000,000×5%×(1/4)=$25,000 interest payment. b. You profit from your futures investment.The settlement price of your futures contract is 95 (=100-5). Your profit earned on the futures position is calculated as [95-94] ×(1/100) ×(1/4) ×$1,000,000×2=$5,000. Your total return is then $25,000+$5,000=$30,000.

Eurodollar Futures Hedge if You are an Investor * 2. What happens if the 3-month LIBOR is 7% p.a. on Sept. 2003?a. You deposit your $2,000,000 at that realized interest rate 7% p.a., which gives you $2,000,000×7%×(1/4)=$35,000 interest payment. b. You lose from your futures investment.The settlement price of your futures contract is 93 (=100-7). Your profit earned on the futures position is calculated as [93-94] ×(1/100) ×(1/4) ×$1,000,000×2=-$5,000. Your total return is then $35,000-$5,000=$30,000.

Eurodollar Futures Hedge if You are a Borrower * • You are a treasurer of a MNC, and expect to borrow $2,000,000 for 90 days on Sept. 17, 2003, because of your imports on that day.. • Today, the settlement price of the Sept03 interest rate futures is 94.00. • If you are uncertain about what your interest cost will be, and wish to lock the cost of your loan. How will you hedge against this interest rate risk? (You are worrying that the prevailing interest rate on that day will be very high.)

Eurodollar Futures Hedge if You are a Borrower * • You will sell (short) 2 Euro dollar interest rate futures contracts at 94.00. This means that you can lock your cost of borrowing at 6% p.a. (that is, you lock your interest cost at $2,000,000×6%×(90/360)=$30,000.) • We will demonstrate that no matter what the realized interest rate at Sept. 17 2003 is, your interest cost is not altered since you’ve hedged your interest rate risk.

Eurodollar Futures Hedge if You are a Borrower * 1. What happens if the 3-month LIBOR is 5% p.a. on Sept. 2003?a. You borrow $2,000,000 at that realized interest rate 5% p.a., which yields $2,000,000×5%×(1/4)=$25,000 interest cost. b. You lose from your futures investment.The settlement price of your futures contract is 95 (=100-5). Your profit earned on the futures position is calculated as [94-95] ×(1/100) ×(1/4) ×$1,000,000×2=-$5,000. Your total cost is then $25,000+$5,000=$30,000.

Eurodollar Futures Hedge if You are a Borrower * 2. What happens if the 3-month LIBOR is 7% p.a. on Sept. 2003?a. You borrow $2,000,000 at that realized interest rate 7% p.a., which yields $2,000,000×7%×(1/4)=$35,000 interest cost. b. You profit from your futures investment.The settlement price of your futures contract is 93 (=100-7). Your profit earned on the futures position is calculated as [94-93] ×(1/100) ×(1/4) ×$1,000,000×2=$5,000. Your total cost is then $35,000-$5,000=$30,000.

Options Contracts: Preliminaries • An option gives the holder the right, but not the obligation, to buy (call) or sell (put) a given quantity (contract size) of an asset (underlying asset) in the future (expiration date), at prices (strike price) agreed upon today. • The price specified in the contract is called the strike or exercise price. The specified maturity date is called the expiration date. The price paid for the option is called the option premium.

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.

Types of Contracts Examples • An American call option on spot € : • The right to buy € 1 million for $1.10 per € from today until expiration on Dec 15, 2001. • This “call on €” is also a “put on US$”. • A European put option on Swiss franc futures : • The right to sell SFr 10 million March 2002 futures for $0.65 per SFr on (and only on) Mar 15, 2002. • This “put on SFr” is also a “call on US$”.

Options Contracts: Preliminaries • In-the-money (it’s worthwhile exercising your option) • Call: ST>E • Put: ST<E • At-the-money (you’re indifferent whether you exercise the option) • Call: ST=E • Put: ST=E • Out-of-the-money (you will not exercise your option) • Call: ST<E • Put: ST>E

Currency Options • Currency options began trading on the Philadelphia Stock Exchange (PHLX) in 1982. • Since then, the markets have expanded : • more option exchanges around the world, • more currencies and debt instruments on which options are traded, • option contracts with longer maturities, • more “styles” of option contracts, and • greater volume of trading activity.

62,500 PHLX Currency Option Specifications

OTC Organized Exchanges 1995 1998 1995 1998 Currency Options $41.0 $87.1 $3.8 $1.8 Location and Scale of Trading • Currency options are traded by banks on an over-the-counter (OTC) basis and on organized futures and options exchanges. • According to surveys conducted by the Bank for International Settlements, the volume of trading in terms of billions per day is:

Currency Futures Options • Are an option on a currency futures contract. • Exercise of a currency futures option results in a long futures position for the holder of a call or the writer of a put. • Exercise of a currency futures option results in a short futures position for the seller of a call or the buyer of a put. • If the futures position is not offset prior to its expiration, foreign currency will change hands.

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]

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]

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

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

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

INTERNATIONAL FINANCIAL MANAGEMENT