Chapter Objective: This chapter discusses exchange-traded currency futures contracts, options contracts, and options on currency futures. 6 Chapter Six Futures and Options on Foreign Exchange 6-0

Chapter Outline Futures Contracts: Preliminaries Currency Futures Markets Basic Currency Futures Relationships Options Contracts: Preliminaries Currency Options Markets Currency Futures Options Basic Option Pricing Relationships at Expiry 6-1

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 a price 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. 6-2

Futures Contracts: Preliminaries Standardizing Features: Contract Size Delivery Month Daily resettlement Initial performance bond (referred to as initial margin, about 2 to 10 percent of contract value, cash or T-bills held at your brokerage account): works together with the mechanism of daily settlement to avoid the default risk which forwards trading suffers from. 6-3

Daily Resettlement: An Example Consider a long position in the CME’s U.S. Dollar / Euro contract. It is written on €125,000 and quoted in $ per €. The strike price is $1.30 (it is a jargon used for options; normally we don’t use it for futures; it simply means the trading price of your long or short futures position here) the maturity is 3 months. At initiation of the contract, the long posts an initial margin of $6,500. The maintenance performance bond (referred to as maintenance margin is $4,000). 6-4

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,

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 (strike, settlement) price with one-day-shorter maturity. 6-6

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 will receive a margin call from his brokerage account executive. He has a decision to make: he can maintain his long position only by adding more funds back to the initial margin level—if he fails to do so, his position will be closed out automatically with an offsetting short position. 6-7

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

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. $1,250 –$1,250 $1.31 $1.30 $1.27 $1.26 $1.24 –$3,750 –$1,250 –$2,500 Gain/LossSettle $7,750 $6,500 $2,750 + $3,750 = $6,500 $5,250 $2,750 Account Balance = $6,500 – $1,

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) 6-10

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

Currency Futures Markets The Chicago Mercantile Exchange (CME) Group (including CBOT & NYMEX) 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 6-12

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. 6-13

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. 6-14

Reading Currency Futures Quotes OPENHIGHLOWSETTLECHG OPEN INT Euro/US Dollar (CME)—€125,000; $ per € Mar172, Jun2,266 Highest price that day Lowest price that day Closing price Daily Change Number of open contracts Expiry month Opening price 6-15

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. 6-16

Reading Currency Futures Quotes Notice that open interest is greatest in the nearby contract, in this case March, In general, open interest typically decreases with term to maturity of most futures contracts. OPENHIGHLOWSETTLECHG OPEN INT Euro/US Dollar (CME)—€125,000; $ per € Mar172, Jun2,

Basic Currency Futures Relationships The holder of a long position is committing himself to pay $ per euro for €125,000—a $184, position. As there are 172,396 such contracts outstanding, this represents a notional principal of over $31.8 billion! OPENHIGHLOWSETTLECHG OPEN INT Euro/US Dollar (CME)—€125,000; $ per € Mar172, Jun2,

Reading Currency Futures Quotes 1 + i € 1 + i $ F($/€) S($/€) = Recall from chapter 6, our interest rate parity condition: OPENHIGHLOWSETTLECHG OPEN INT Euro/US Dollar (CME)—€125,000; $ per € Mar172, Jun2,

Reading Currency Futures Quotes From March to June 2008 we should expect lower interest rates in dollar denominated accounts. OPENHIGHLOWSETTLECHG OPEN INT Euro/US Dollar (CME)—€125,000; $ per € Mar172, Jun2,

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. 6-21

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. American options are usually worth more than European options, other things equal. ……Why?  Moneyness –If immediate exercise is profitable, an option is “in the money.” –Out of the money options can still have (time) value. 6-22

Call 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. 6-23

Options Contracts: Preliminaries Intrinsic Value The difference between the exercise price of the option and the spot price of the underlying asset. Time (or Speculative) Value The difference between the option premium and the intrinsic value of the option. Option Premium = Intrinsic Value Time Value

PHLX Currency Option Specifications CurrencyContract Size Australian dollarAUD 10,000 British poundGBP 10,000 Canadian dollarCAD 10,000 EuroEUR 10,000 Japanese yenJPY 1,000,000 Mexican pesoMXN 100,000 New Zealand dollarNZD 10,000 Norwegian kroneNOK 100,000 South African randZAR 100,000 Swedish kronaSEK 100,000 Swiss francCHF 10,

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 S T – E. If the call is out-of-the-money, it is worthless. C aT = C eT = Max[S T - E, 0] 6-26

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 - S T. If the put is out-of-the-money, it is worthless. P aT = P eT = Max[E – S T, 0] 6-27

Basic Option Profit Profiles E STST Profit loss –c0–c0 E + c 0 Long 1 call If the call is in-the- money, it is worth S T – E. If the call is out-of- the-money, it is worthless and the buyer of the call loses his entire investment of c 0. In-the-moneyOut-of-the-money Owner of the call 6-28

Basic Option Profit Profiles E STST Profit loss c0c0 E + c 0 short 1 call If the call is in-the- money, the writer loses S T – E. If the call is out-of- the-money, the writer keeps the option premium. In-the-moneyOut-of-the-money Seller of the call 6-29

Basic Option Profit Profiles E STST Profit loss – p 0 E – p 0 long 1 put E – p 0 If the put is in- the-money, it is worth E – S T. The maximum gain is E – p 0 If the put is out- of-the-money, it is worthless and the buyer of the put loses his entire investment of p 0. Out-of-the-moneyIn-the-money Owner of the put 6-30

Basic Option Profit Profiles E STST Profit loss p 0 E – p 0 short 1 put – E + p 0 If the put is in- the-money, it is worth E –S T. The maximum loss is – E + p 0 If the put is out- of-the-money, it is worthless and the seller of the put keeps the option premium of p 0. Seller of the put 6-31

ExampleX $1.50 STST Profit loss –$0.25 $1.75 Long 1 call on €1 Consider a call option on €1. The option premium is $0.25 per € The exercise price is $1.50 per €. 6-32

ExampleX $1.50 STST Profit loss –$7, $1.75 Long 1 call on €31,250 Consider a call option on €31,250. The option premium is $0.25 per € The exercise price is $1.50 per €. 6-33

ExampleX $1.50 STST Profit loss $42, $1.35 Long 1 put on €31,250 Consider a put option on €31,250. The option premium is $0.15 per € The exercise price is $1.50 per euro. What is the maximum gain on this put option? At what exchange rate do you break even? –$4, $42, = €31,250×($1.50 – $0.15)/€ $4, = €31,250×($0.15)/€ 6-34

American Option Pricing RelationshipsX 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: C aT > C eT = Max[S T - E, 0] P aT > P eT = Max[E - S T, 0] 6-35

Market Value, Time Value and Intrinsic Value for an American Call X E STST Profit loss Long 1 call 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. Intrinsic value Time value Market Value In-the-moneyOut-of-the-money 6-36

Theoretical Price of European Call for Foreign Currency

Theoretical Price of European Call for Stock – Nobel Prize Formula