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Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedINTERNATIONALFINANCIALMANAGEMENTEUN/RESNICKSecondEdition9Chapte

rNineFuturesandOptionsonForeignExchangeChapterObjective:Thischapterdiscussesexchange-tradedcurrencyfuturescontracts,optionscon

tracts,andoptionsoncurrencyfutures.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedChapterOutline⚫FuturesContrac

ts:Preliminaries⚫CurrencyFuturesMarkets⚫BasicCurrencyFuturesRelationships⚫EurodollarInterestRateFuturesContracts⚫OptionsContracts:Prelimina

ries⚫CurrencyOptionsMarkets⚫CurrencyFuturesOptionsIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrig

htsreservedChapterOutline(continued)⚫BasicOptionPricingRelationshipsatExpiry⚫AmericanOptionPricingRelationships⚫EuropeanOptionPricingRelationships⚫B

inomialOptionPricingModel⚫EuropeanOptionPricingModel⚫EmpiricalTestsofCurrencyOptionModelsIrwin/McGraw

-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedFuturesContracts:Preliminaries⚫Afuturescontractislikeaforwardcontract:◼Itspecifies

thatacertaincurrencywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.⚫Afuturescontra

ctisdifferentfromaforwardcontract:◼Futuresarestandardizedcontractstradingonorganizedexchangeswithdailyresettlementthroughaclearingh

ouse.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedFuturesContracts:Pr

eliminaries⚫StandardizingFeatures:◼ContractSize◼DeliveryMonth◼Dailyresettlement⚫InitialMargin(about4%ofcontr

actvalue,cashorT-billsheldinastreetnameatyourbrokers).Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyRes

ettlement:AnExample⚫Supposeyouwanttospeculateonariseinthe$/¥exchangerate(specificallyyouthinkthatthedo

llarwillappreciate).Currently$1=¥140.The3-monthforwardpriceis$1=¥150.CurrencyperU.S.$equivalentU.S.$WedTueWedTueJapan(yen)0

.0071428570.0071942451401391-monthforward0.0069930070.0070422541431423-monthsforward0.0066666670.0067114091501496-monthsforward0.0062

50.006289308160159Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExample⚫Curren

tly$1=¥140anditappearsthatthedollarisstrengthening.⚫Ifyouenterintoa3-monthfuturescontracttosell¥attherateof$1=¥150youwillma

kemoneyiftheyendepreciates.Thecontractsizeis¥12,500,000⚫Yourinitialmarginis4%ofthecontractvalue:?50$10?2,500,00.04$3,333.33=Irwin/McGraw

-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExampleIftomorrow,thefuturesrate

closesat$1=¥149,thenyourposition’svaluedrops.Youroriginalagreementwastosell¥12,500,000andreceive$83,333.33Butnow¥1

2,500,000isworth$83,892.62?49$10?2,500,0062.892,83$=Youhavelost$559.28overnight.Irwin/McGraw-HillCopyrigh

t©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExample⚫The$559.28comesoutofyour$3,333.33margina

ccount,leaving$2,774.05⚫Thisisshortofthe$3,355.70requiredforanewposition.?49$10?2,500,00.04$3,355.70=⚫Yourbrok

erwillletyouslideuntilyourunthroughyourmaintenancemargin.Thenyoumustpostadditionalfundsoryourpositionwillbeclosedo

ut.Thisisusuallydonewithareversingtrade.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allr

ightsreservedCurrencyFuturesMarkets⚫TheChicagoMercantileExchange(CME)isbyfarthelargest.⚫Othersinclude:◼ThePhiladelphiaBoardof

Trade(PBOT)◼TheMidAmericacommoditiesExchange◼TheTokyoInternationalFinancialFuturesExchange◼TheLondonInternationalFinancialFuturesExchangeIrwin/M

cGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedTheChicagoMercantileExchange⚫Expirycycl

e:March,June,September,December.⚫Deliverydate3rdWednesdayofdeliverymonth.⚫Lasttradingdayisthesecondbusine

ssdayprecedingthedeliveryday.⚫CMEhours7:20a.m.to2:00p.m.CST.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsrese

rvedCMEAfterHours⚫Extended-hourstradingonGLOBEXrunsfrom2:30p.m.to4:00p.mdinnerbreakandthenbackatitfrom6:00p.m.t

o6:00a.m.CST.⚫SingaporeInternationalMonetaryExchange(SIMEX)offerinterchangeablecontracts.⚫There’sothermarke

ts,butnoneareclosetoCMEandSIMEXtradingvolume.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicCurrenc

yFuturesRelationships⚫OpenInterestreferstothenumberofcontractsoutstandingforaparticulardeliverymonth.⚫Openinterestisagoodproxyfo

rdemandforacontract.⚫Somerefertoopeninterestasthedepthofthemarket.Thebreadthofthemarketwouldbehowmanydifferentcontracts(expirymonth,cur

rency)areoutstanding.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedReadingaFuturesQuoteOpenHiLoSettleChangeLifetim

eHighLifetimeLowOpenInterestSept.9282.9325.9276.9309+.00271.2085.863674,639ExpirymonthOpeningpriceHighestpricethatdayLowe

stpricethatdayClosingpriceDailyChangeHighestandlowestpricesoverthelifetimeofthecontract.NumberofopencontractsIrwin/McGraw-HillCopyright©2001byThe

McGraw-HillCompanies,Inc.AllrightsreservedEurodollarInterestRateFuturesContracts⚫Widelyusedfuturescontractforh

edgingshort-termU.S.dollarinterestraterisk.⚫Theunderlyingassetisahypothetical$1,000,00090-dayEurodollardeposit—theco

ntractiscashsettled.⚫TradedontheCMEandtheSingaporeInternationalMonetaryExchange.⚫ThecontracttradesintheMarch,June,SeptemberandDecembercycle.I

rwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedReadingEurodollarFuturesQuotesEURODOLLAR(CME)—$1million

;ptsof100%OpenHighLowSettleChgYieldSettleChangeOpenInterestJuly94.6994.6994.6894.68-.015.32+.0147,417Eurodollarfu

turespricesarestatedasanindexnumberofthree-monthLIBORcalculatedasF=100-LIBOR.TheclosingpricefortheJulycontrac

tis94.68thustheimpliedyieldis5.32percent=100–98.68Thechangewas.01percentof$1millionrepresenting$100onanannualbasis.Sinceitisa3-monthcontracto

nebasispointcorrespondstoa$25pricechange.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionsContracts:Prelimi

naries⚫Anoptiongivestheholdertheright,butnottheobligation,tobuyorsellagivenquantityofanassetinthefuture,atpricesagreedupontoday.⚫Callsvs.Put

s◼Calloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpric

esagreedupontoday.◼Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofsomeassetatsometimeinthefuture,atprice

sagreedupontoday.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionsContracts:Preli

minaries⚫Europeanvs.Americanoptions◼Europeanoptionscanonlybeexercisedontheexpirationdate.◼Americanoptionscanbeex

ercisedatanytimeuptoandincludingtheexpirationdate.◼Sincethisoptiontoexerciseearlygenerallyhasvalue,Americanoptio

nsareusuallyworthmorethanEuropeanoptions,otherthingsequal.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,In

c.AllrightsreservedOptionsContracts:Preliminaries⚫In-the-money◼Theexercisepriceislessthanthespotpriceoftheunderlyin

gasset.⚫At-the-money◼Theexercisepriceisequaltothespotpriceoftheunderlyingasset.⚫Out-of-the-money◼Theexercisepriceismorethanthespotpriceoftheunde

rlyingasset.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionsContracts:Preli

minaries⚫IntrinsicValue◼Thedifferencebetweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.⚫SpeculativeValue

◼Thedifferencebetweentheoptionpremiumandtheintrinsicvalueoftheoption.OptionPremium=IntrinsicValueSpeculati

veValue+Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedCurrencyOptionsMarkets⚫PHLX⚫HKFE⚫2

0-hourtradingday.⚫OTCvolumeismuchbiggerthanexchangevolume.⚫TradingisinsevenmajorcurrenciesplustheeuroagainsttheU.S.dollar.Irwin/McGraw-HillCopyrig

ht©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedPHLXCurrencyOptionSpecificationsCurrencyContractSizeAustraliandollarAD50,000Br

itishpound£31,250CanadiandollarCD50,000DeutschemarkDM62,500FrenchfrancFF250,000Japaneseyen¥6,250,000Sw

issfrancSF62,500Euro62,500Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedCurrencyFuturesOptions⚫Areanoptiononac

urrencyfuturescontract.⚫Exerciseofacurrencyfuturesoptionresultsinalongfuturespositionfortheholderofacallorthewriterofaput.⚫Exerciseofacur

rencyfuturesoptionresultsinashortfuturespositionforthesellerofacallorthebuyerofaput.⚫Ifthefuturespositionisnotoffsetpri

ortoitsexpiration,foreigncurrencywillchangehands.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasic

OptionPricingRelationshipsatExpiry⚫Atexpiry,anAmericancalloptionisworththesameasaEuropeanoptionwiththesamecharacteristics.⚫Ifthecallisin-the-money,it

isworthST–E.⚫Ifthecallisout-of-the-money,itisworthless.CaT=CeT=Max[ST-E,0]Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allright

sreservedBasicOptionPricingRelationshipsatExpiry⚫Atexpiry,anAmericanputoptionisworththesameasaEuropeanoptionwiththesamecha

racteristics.⚫Iftheputisin-the-money,itisworthE-ST.⚫Iftheputisout-of-the-money,itisworthless.PaT=PeT=Max[E-

ST,0]Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]pr

ofitlossEE+CSTIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]

profitlossEE+CSTIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicOptionProfitProfiles

PaT=PeT=Max[E-ST,0]profitlossEE-pSTIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicOpti

onProfitProfilesCaT=CeT=Max[ST-E,0]profitlossESTE-pIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrig

htsreservedAmericanOptionPricingRelationships⚫WithanAmericanoption,youcandoeverythingthatyoucandowithaEuropeanoption—thisopti

ontoexerciseearlyhasvalue.CaT>CeT=Max[ST-E,0]PaT>PeT=Max[E-ST,0]Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedMa

rketValue,TimeValueandIntrinsicValueforanAmericanCallCaT>Max[ST-E,0]ProfitlossESTMarketValueIntrinsicvalu

eTimevalueOut-of-the-moneyIn-the-moneyIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptio

nPricingRelationshipsConsidertwoinvestments1BuyacalloptionontheBritishpoundfuturescontract.Thecashflowtodayis-Ce2Replicatetheup

sidepayoffofthecallby1BorrowingthepresentvalueoftheexercisepriceofthecallintheU.S.ati$ThecashflowtodayisE/(1+i$)2Lendingthepre

sentvalueofSTati£Thecashflowis-ST/(1+i£)Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOp

tionPricingRelationshipsWhentheoptionisin-the-moneybothstrategieshavethesamepayoff.Whentheoptionisout-of-the-moneyithasahigherpayo

fftheborrowingandlendingstrategy.Thus:0,)1()1(max$£+−+iEiSCTeIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedE

uropeanOptionPricingRelationshipsUsingasimilarportfoliotoreplicatetheupsidepotentialofaput,wecanshowthat:0,)1()1(max£$+−+iSiEPTeIrwin/McGraw-

HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBinomialOptionPricingModel⚫Imaginea

simpleworldwherethedollar-euroexchangerateisS0($/)=$1todayandinthenextyear,S1($/)iseither$1.1or$.90.$1$.90$

1.10S0($/)S1($/)Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10

$0C1($/)⚫AcalloptionontheeurowithexercisepriceS0($/)=$1willhavethefollowingpayoffs.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCom

panies,Inc.Allrightsreserved$1$.90$1.10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModel⚫Wecanreplicate

thepayoffsofthecalloption.Withaleveredpositionintheeuro.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrigh

tsreserved$1$.90$1.10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModeldebt-$.90-$.90portfolio$.20$.00Borrow

thepresentvalueof$.90todayandbuy1.Yournetpayoffinoneperiodiseither$.2or$0.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompani

es,Inc.AllrightsreservedBinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00⚫Theportfoliohastwicetheo

ption’spayoffsotheportfolioisworthtwicethecalloptionvalue.Irwin/McGraw-HillCopyright©2001byTheMcGraw-Hi

llCompanies,Inc.Allrightsreserved$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00BinomialOptionPricingModelTheportfoliov

aluetodayistoday’svalueofoneeurolessthepresentvalueofa$.90debt:)1(90$.1$$i+−Irwin/McGraw-HillCopyrigh

t©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)d

ebt-$.90-$.90portfolio$.20$.00Wecanvaluetheoptionashalfofthevalueoftheportfolio:+−=)1(90$.1$21$0iCIr

win/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBinomialOptionPricingModel⚫Themostimportantlessonfromthebinomia

loptionpricingmodelis:thereplicatingportfoliointuition.⚫Manyderivativesecuritiescanbevaluedbyvaluingportfoliosofprimitivesecuritieswhenthosepor

tfolioshavethesamepayoffsasthederivativesecurities.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsrese

rvedEuropeanOptionPricingFormula⚫Wecanusethereplicatingportfoliointuitiondevelopedinthebinomialoptionpricingformulatoge

nerateafaster-to-usemodelthataddressesamuchmorerealisticworld.Irwin/McGraw-HillCopyright©2001byTheMcGraw-H

illCompanies,Inc.AllrightsreservedEuropeanOptionPricingFormulaThemodelisTredNEdNFC$)]()([210−−=WhereC0=thevalueofaEurope

anoptionattimet=0TrrteSF)(£$−=r$=theinterestrateavailableintheU.S.r£=theinterestrateavailableintheforeigncountry—inthiscaseth

eU.K.,5.)/ln(21TTEFd+=Tdd−=12Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropea

nOptionPricingFormulaFindthevalueofasix-monthcalloptionontheBritishpoundwithanexercisepriceof$1.50=£

1Thecurrentvalueofapoundis$1.60TheinterestrateavailableintheU.S.isr$=5%.TheinterestrateintheU.K.isr£=7%.Theoptionmaturityis

6months(halfofayear).Thevolatilityofthe$/£exchangerateis30%p.a.Beforewestart,notethattheintrinsicvalueoftheoptionis$.10—ouranswermustbeat

leastthat.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingFormulaLet’

stryourhandatusingthemodel.Ifyouhaveacalculatorhandy,followalong.Then,calculated1andd2106066.05.4.5.)4.0(5.)50.1/485075.1ln(5.)

/ln(221=+=+=TTEFdFirstcalculate485075.150.150.0)07.05(.)(£$===−−eeSFTrrt176878.05.4.106066.012−=−=−=Td

dIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingFormulaN(d1)=N(0.106066)=.5422N(d2)

=N(-0.1768)=0.4298TredNEdNFC$)]()([210−−=157.0$]4298.50.15422.485075.1[5.*05.0=−=−eC485075.1=F10606

6.01=d176878.02−=dIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionValueDeterminantsCallPut1.Exchangerate+–

2.Exerciseprice–+3.InterestrateinU.S.+–4.Interestrateinothercountry+–5.Variabilityinexchangerate++6.

Expirationdate++ThevalueofacalloptionC0mustfallwithinmax(S0–E,0)<C0<S0.Theprecisepositionwilldependontheabovefactors.Irwin/McGraw-HillCopyright©

2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEmpiricalTestsTheEuropeanoptionpricingmodelworksfairlywellinpricingAmericancurrencyoption

s.Itworksbestforout-of-the-moneyandat-the-moneyoptions.Whenoptionsarein-the-money,theEuropeanoptionpricingmodel

tendstounderpriceAmericanoptions.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEndChapter

Nine