1、INTERNATIONALFINANCIALMANAGEMENTEUN/RESNICKSecond Edition9Chapter NineFutures and Options on Foreign ExchangeChapter Objective:This chapter discusses exchange-traded currency futures contracts,options contracts,and options on currency futures.Chapter OutlinelFutures Contracts:PreliminarieslCurrency
2、Futures MarketslBasic Currency Futures RelationshipslEurodollar Interest Rate Futures ContractslOptions Contracts:PreliminarieslCurrency Options MarketslCurrency Futures OptionsChapter Outline(continued)lBasic Option Pricing Relationships at ExpirylAmerican Option Pricing RelationshipslEuropean Opti
3、on Pricing RelationshipslBinomial Option Pricing ModellEuropean Option Pricing ModellEmpirical Tests of Currency Option ModelsDaily Resettlement:An ExamplelSuppose you want to speculate on a rise in the$/exchange rate(specifically you think that the dollar will appreciate).Currently$1=140.The 3-mont
4、h forward price is$1=150.Currency per U.S.$equivalent U.S.$WedTueWedTueJapan(yen)0.0071428570.0071942451401391-month forward0.0069930070.0070422541431423-months forward0.0066666670.0067114091501496-months forward0.006250.006289308160159Daily Resettlement:An ExamplelCurrently$1=140 and it appears tha
5、t the dollar is strengthening.lIf 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 12,500,000lYour initial margin is 4%of the contract value:150$1012,500,00.04$3,333.33 Daily Resettlement:An ExampleIf tomorrow,the
6、futures rate closes at$1=149,then your positions value drops.Your original agreement was to sell 12,500,000 and receive$83,333.33But now 12,500,000 is worth$83,892.62149$1012,500,0062.892,83$You have lost$559.28 overnight.Daily Resettlement:An ExamplelThe$559.28 comes out of your$3,333.33 margin acc
7、ount,leaving$2,774.05lThis is short of the$3,355.70 required for a new position.149$1012,500,00.04$3,355.70 lYour 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 trad
8、e.Currency Futures MarketslThe Chicago Mercantile Exchange(CME)is by far the largest.lOthers include:nThe Philadelphia Board of Trade(PBOT)nThe MidAmerica commodities ExchangenThe Tokyo International Financial Futures ExchangenThe London International Financial Futures ExchangeThe Chicago Mercantile
9、 ExchangelExpiry cycle:March,June,September,December.lDelivery date 3rd Wednesday of delivery month.lLast trading day is the second business day preceding the delivery day.lCME hours 7:20 a.m.to 2:00 p.m.CST.CME After HourslExtended-hours trading on GLOBEX runs from 2:30 p.m.to 4:00 p.m dinner break
10、 and then back at it from 6:00 p.m.to 6:00 a.m.CST.lSingapore International Monetary Exchange(SIMEX)offer interchangeable contracts.lTheres other markets,but none are close to CME and SIMEX trading volume.Basic Currency Futures RelationshipslOpen Interest refers to the number of contracts outstandin
11、g for a particular delivery month.lOpen interest is a good proxy for demand for a contract.lSome 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 Open Hi Lo Settle Change Li
12、fetime High Lifetime Low Open Interest Sept.9282.9325.9276.9309+.0027 1.2085.8636 74,639 Expiry monthOpening priceHighest price that dayLowest price that dayClosing priceDaily ChangeHighest and lowest prices over the lifetime of the contract.Number of open contracts Eurodollar Interest Rate Futures
13、ContractslWidely used futures contract for hedging short-term U.S.dollar interest rate risk.lThe underlying asset is a hypothetical$1,000,000 90-day Eurodollar depositthe contract is cash settled.lTraded on the CME and the Singapore International Monetary Exchange.lThe contract trades in the March,J
14、une,September and December cycle.Reading Eurodollar Futures QuotesEURODOLLAR(CME)$1 million;pts of 100%OpenHighLowSettleChgYieldSettle ChangeOpen InterestJuly94.6994.6994.6894.68-.015.32+.0147,417 Eurodollar futures prices are stated as an index number of three-month LIBOR calculated as F=100-LIBOR.
15、The closing price for the July contract is 94.68 thus the implied yield is 5.32 percent=100 98.68The 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.Options Contracts:PreliminarieslAn option gives
16、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.lCalls vs.PutsnCall 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
17、.nPut 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.Options Contracts:PreliminarieslEuropean vs.American optionsnEuropean options can only be exercised on the expiration date.nAmerican options c
18、an be exercised at any time up to and including the expiration date.nSince this option to exercise early generally has value,American options are usually worth more than European options,other things equal.Options Contracts:PreliminarieslIn-the-moneynThe exercise price is less than the spot price of
19、 the underlying asset.lAt-the-moneynThe exercise price is equal to the spot price of the underlying asset.lOut-of-the-moneynThe exercise price is more than the spot price of the underlying asset.Options Contracts:PreliminarieslIntrinsic ValuenThe difference between the exercise price of the option a
20、nd the spot price of the underlying asset.lSpeculative ValuenThe difference between the option premium and the intrinsic value of the option.Option Premium=Intrinsic ValueSpeculative Value+Currency Options MarketslPHLXlHKFEl20-hour trading day.lOTC volume is much bigger than exchange volume.lTrading
21、 is in seven major currencies plus the euro against the U.S.dollar.PHLX Currency Option SpecificationsCurrencyContract SizeAustralian dollarAD50,000British pound31,250Canadian dollarCD50,000Deutsche markDM62,500French francFF250,000Japanese yen6,250,000Swiss francSF62,500Euro62,500Currency Futures O
22、ptionslAre an option on a currency futures contract.lExercise of a currency futures option results in a long futures position for the holder of a call or the writer of a put.lExercise of a currency futures option results in a short futures position for the seller of a call or the buyer of a put.lIf
23、the futures position is not offset prior to its expiration,foreign currency will change hands.Basic Option Pricing Relationships at ExpirylAt expiry,an American call option is worth the same as a European option with the same characteristics.lIf the call is in-the-money,it is worth ST E.lIf the call
24、 is out-of-the-money,it is worthless.CaT=CeT=MaxST-E,0Basic Option Pricing Relationships at ExpirylAt expiry,an American put option is worth the same as a European option with the same characteristics.lIf the put is in-the-money,it is worth E-ST.lIf the put is out-of-the-money,it is worthless.PaT=Pe
25、T=MaxE-ST,0Basic Option Profit ProfilesCaT=CeT=MaxST-E,0profitlossEE+CSTLong 1 callBasic Option Profit ProfilesCaT=CeT=MaxST-E,0profitlossEE+CSTshort 1 callBasic Option Profit ProfilesPaT=PeT=MaxE-ST,0profitlossEE-pSTlong 1 putBasic Option Profit ProfilesCaT=CeT=MaxST-E,0profitlossESTShort 1 putE-pA
26、merican Option Pricing RelationshipslWith an American option,you can do everything that you can do with a European optionthis option to exercise early has value.CaT CeT=MaxST-E,0PaT PeT=MaxE-ST,0Market Value,Time Value and Intrinsic Value for an American CallCaT MaxST-E,0ProfitlossESTMarket ValueInt
27、rinsic valueST-ETime valueOut-of-the-moneyIn-the-moneyEuropean Option Pricing RelationshipsConsider two investments1Buy a call option on the British pound futures contract.The cash flow today is-Ce2Replicate the upside payoff of the call by 1Borrowing the present value of the exercise price of the c
28、all in the U.S.at i$The cash flow today is E/(1+i$)2Lending the present value of ST at i The cash flow is -ST/(1+i)European Option Pricing RelationshipsWhen the option is in-the-money both strategies have the same payoff.When the option is out-of-the-money it has a higher payoff the borrowing and le
29、nding strategy.Thus:0,)1()1(max$iEiSCTeEuropean Option Pricing RelationshipsUsing a similar portfolio to replicate the upside potential of a put,we can show that:0,)1()1(max$iSiEPTeBinomial Option Pricing ModellImagine a simple world where the dollar-euro exchange rate is S0($/)=$1 today and in the
30、next year,S1($/)is either$1.1 or$.90.$1$.90$1.10S0($/)S1($/)Binomial Option Pricing Model$1$.90$1.10S0($/)S1($/)$.10$0C1($/)lA call option on the euro with exercise price S0($/)=$1 will have the following payoffs.$1$.90$1.10S0($/)S1($/)$.10$0C1($/)Binomial Option Pricing ModellWe can replicate the p
31、ayoffs of the call option.With a levered position in the euro.$1$.90$1.10S0($/)S1($/)$.10$0C1($/)Binomial Option Pricing Modeldebt-$.90-$.90portfolio$.20$.00Borrow the present value of$.90 today and buy 1.Your net payoff in one period is either$.2 or$0.Binomial Option Pricing Model$1$.90$1.10S0($/)S
32、1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00lThe portfolio has twice the options payoff so the portfolio is worth twice the call option value.$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00Binomial Option Pricing Model The portfolio value today is todays value of one euro less
33、 the present value of a$.90 debt:)1(90$.1$iBinomial Option Pricing Model$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00We can value the option as half of the value of the portfolio:)1(90$.1$21$0iCBinomial Option Pricing ModellThe most important lesson from the binomial option pric
34、ing model is:lMany derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.European Option Pricing FormulalWe can use the replicating portfolio intuition developed in the binomial option pricing formul
35、a to generate a faster-to-use model that addresses a much more realistic world.European Option Pricing FormulaThe model isTredNEdNFC$)()(210WhereC0=the value of a European option at time t=0TrrteSF)($r$=the interest rate available in the U.S.r =the interest rate available in the foreign countryin th
36、is case the U.K.,5.)/ln(21TTEFdTdd12European Option Pricing FormulaFind the value of a six-month call option on the British pound with an exercise price of$1.50=1The current value of a pound is$1.60The interest rate available in the U.S.is r$=5%.The interest rate in the U.K.is r =7%.The option matur
37、ity is 6 months(half of a year).The volatility of the$/exchange rate is 30%p.a.Before we start,note that the intrinsic value of the option is$.10our answer must be at least that.European Option Pricing FormulaLets try our hand at using the model.If you have a calculator handy,follow along.Then,calcu
38、late d1 and d2106066.05.4.5.)4.0(5.)50.1/485075.1ln(5.)/ln(221TTEFdFirst calculate485075.150.150.0)07.05(.)($eeSFTrrt176878.05.4.106066.012TddEuropean Option Pricing FormulaN(d1)=N(0.106066)=.5422N(d2)=N(-0.1768)=0.4298TredNEdNFC$)()(210157.0$4298.50.15422.485075.1 5.*05.0eC485075.1F106066.01d176878
39、.02dOption Value DeterminantsCall Put1.Exchange rate+2.Exercise price +3.Interest rate in U.S.+4.Interest rate in other country+5.Variability in exchange rate+6.Expiration date+The value of a call option C0 must fall within max(S0 E,0)C0 S0.The precise position will depend on the above factors.Empirical TestsThe European option pricing model works fairly well in pricing American currency options.It works best for out-of-the-money and at-the-money options.When options are in-the-money,the European option pricing model tends to underprice American options.End Chapter Nine
