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Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedINTERNATIONALFINANCIALMANAGEMENTEUN/RESNICKSecondEdition9ChapterNi

neFuturesandOptionsonForeignExchangeChapterObjective:Thischapterdiscussesexchange-tradedcurrencyfuturescontracts,optionscontrac

ts,andoptionsoncurrencyfutures.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedChapterOutline⚫F

uturesContracts:Preliminaries⚫CurrencyFuturesMarkets⚫BasicCurrencyFuturesRelationships⚫EurodollarInterestRateFuturesContracts⚫Option

sContracts:Preliminaries⚫CurrencyOptionsMarkets⚫CurrencyFuturesOptionsIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreser

vedChapterOutline(continued)⚫BasicOptionPricingRelationshipsatExpiry⚫AmericanOptionPricingRelationships⚫EuropeanOptionPricingRelationships⚫Binomi

alOptionPricingModel⚫EuropeanOptionPricingModel⚫EmpiricalTestsofCurrencyOptionModelsIrwin/McGraw-Hill

Copyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedFuturesContracts:Preliminaries⚫Afuturescontractislikeaforwardcontract:◼Itspecifiest

hatacertaincurrencywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.⚫Afuturescontractisdifferentfromafo

rwardcontract:◼Futuresarestandardizedcontractstradingonorganizedexchangeswithdailyresettlementthroughaclearinghouse.Irwin/

McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedFuturesContracts:Preliminaries⚫StandardizingFeatures:◼ContractSiz

e◼DeliveryMonth◼Dailyresettlement⚫InitialMargin(about4%ofcontractvalue,cashorT-billsheldinastreetnameatyourbrokers).Irwin/McGraw-

HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExample⚫Supposeyouwanttospeculateonariseinthe$/¥excha

ngerate(specificallyyouthinkthatthedollarwillappreciate).Currently$1=¥140.The3-monthforwardpriceis$1=¥150.CurrencyperU.S.$eq

uivalentU.S.$WedTueWedTueJapan(yen)0.0071428570.0071942451401391-monthforward0.0069930070.0070422541431423-monthsforward0.0066666670.0

067114091501496-monthsforward0.006250.006289308160159Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompan

ies,Inc.AllrightsreservedDailyResettlement:AnExample⚫Currently$1=¥140anditappearsthatthedollarisstrengthe

ning.⚫Ifyouenterintoa3-monthfuturescontracttosell¥attherateof$1=¥150youwillmakemoneyiftheyendepreciates.Thecontractsi

zeis¥12,500,000⚫Yourinitialmarginis4%ofthecontractvalue:?50$10?2,500,00.04$3,333.33=Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.A

llrightsreservedDailyResettlement:AnExampleIftomorrow,thefuturesrateclosesat$1=¥149,thenyourposition’svalue

drops.Youroriginalagreementwastosell¥12,500,000andreceive$83,333.33Butnow¥12,500,000isworth$83,892.62?49$10?2,500,0062.892,83$=Youhavelost$55

9.28overnight.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExam

ple⚫The$559.28comesoutofyour$3,333.33marginaccount,leaving$2,774.05⚫Thisisshortofthe$3,355.70requiredforanewposition.?49$10?2,500,00.04$3,3

55.70=⚫Yourbrokerwillletyouslideuntilyourunthroughyourmaintenancemargin.Thenyoumustpostadditionalfundsoryo

urpositionwillbeclosedout.Thisisusuallydonewithareversingtrade.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreserv

edCurrencyFuturesMarkets⚫TheChicagoMercantileExchange(CME)isbyfarthelargest.⚫Othersinclude:◼ThePhilade

lphiaBoardofTrade(PBOT)◼TheMidAmericacommoditiesExchange◼TheTokyoInternationalFinancialFuturesExchange◼TheLondonInternationalFinancial

FuturesExchangeIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedTheChicagoMercantileExchange⚫Expirycycl

e:March,June,September,December.⚫Deliverydate3rdWednesdayofdeliverymonth.⚫Lasttradingdayisthesecondbusinessdayprecedingthedeliveryday.⚫CMEh

ours7:20a.m.to2:00p.m.CST.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedCMEAfterHours

⚫Extended-hourstradingonGLOBEXrunsfrom2:30p.m.to4:00p.mdinnerbreakandthenbackatitfrom6:00p.m.to6:00a.m.CST.⚫

SingaporeInternationalMonetaryExchange(SIMEX)offerinterchangeablecontracts.⚫There’sothermarkets,butnoneareclosetoCMEand

SIMEXtradingvolume.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicCurrencyFuturesRelationships⚫OpenInterestre

ferstothenumberofcontractsoutstandingforaparticulardeliverymonth.⚫Openinterestisagoodproxyfordemandforacontract.⚫Somerefertoopenin

terestasthedepthofthemarket.Thebreadthofthemarketwouldbehowmanydifferentcontracts(expirymonth,currency)

areoutstanding.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedReadingaFuturesQuoteOpenHiLoSettleChangeLifet

imeHighLifetimeLowOpenInterestSept.9282.9325.9276.9309+.00271.2085.863674,639ExpirymonthOpeningpriceHighestpricethatdayLowestpri

cethatdayClosingpriceDailyChangeHighestandlowestpricesoverthelifetimeofthecontract.NumberofopencontractsIrwin/McGraw-HillCopyright©200

1byTheMcGraw-HillCompanies,Inc.AllrightsreservedEurodollarInterestRateFuturesContracts⚫Widelyusedfuturescontract

forhedgingshort-termU.S.dollarinterestraterisk.⚫Theunderlyingassetisahypothetical$1,000,00090-dayEurodollardeposit—thecontrac

tiscashsettled.⚫TradedontheCMEandtheSingaporeInternationalMonetaryExchange.⚫ThecontracttradesintheMarch,June,Se

ptemberandDecembercycle.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedReadingEurodollarFuturesQuotesEURODOL

LAR(CME)—$1million;ptsof100%OpenHighLowSettleChgYieldSettleChangeOpenInterestJuly94.6994.6994.6894.68-.015.32

+.0147,417Eurodollarfuturespricesarestatedasanindexnumberofthree-monthLIBORcalculatedasF=100-LIBOR.Theclosingp

ricefortheJulycontractis94.68thustheimpliedyieldis5.32percent=100–98.68Thechangewas.01percentof$1millionrepresenting$100onanannua

lbasis.Sinceitisa3-monthcontractonebasispointcorrespondstoa$25pricechange.Irwin/McGraw-HillCopyright©2001byTheMcGraw-H

illCompanies,Inc.AllrightsreservedOptionsContracts:Preliminaries⚫Anoptiongivestheholdertheright,butnottheobl

igation,tobuyorsellagivenquantityofanassetinthefuture,atpricesagreedupontoday.⚫Callsvs.Puts◼Callopti

onsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpric

esagreedupontoday.◼Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofsomeassetatsometimeinthefut

ure,atpricesagreedupontoday.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionsContracts:Preliminarie

s⚫Europeanvs.Americanoptions◼Europeanoptionscanonlybeexercisedontheexpirationdate.◼Americanoptionscanbe

exercisedatanytimeuptoandincludingtheexpirationdate.◼Sincethisoptiontoexerciseearlygenerallyhasvalue,Americanoptionsareusually

worthmorethanEuropeanoptions,otherthingsequal.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOpti

onsContracts:Preliminaries⚫In-the-money◼Theexercisepriceislessthanthespotpriceoftheunderlyingasset.⚫At-the-money◼Theex

ercisepriceisequaltothespotpriceoftheunderlyingasset.⚫Out-of-the-money◼Theexercisepriceismorethanthespotpriceo

ftheunderlyingasset.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionsContracts:Preliminaries⚫IntrinsicVa

lue◼Thedifferencebetweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.⚫SpeculativeValue◼Thedifference

betweentheoptionpremiumandtheintrinsicvalueoftheoption.OptionPremium=IntrinsicValueSpeculativeValue+Irw

in/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedCurrencyOptionsMarkets⚫PH

LX⚫HKFE⚫20-hourtradingday.⚫OTCvolumeismuchbiggerthanexchangevolume.⚫Tradingisinsevenmajorcurrenciesplusthee

uroagainsttheU.S.dollar.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedPHL

XCurrencyOptionSpecificationsCurrencyContractSizeAustraliandollarAD50,000Britishpound£31,250CanadiandollarCD50,000DeutschemarkDM62,500FrenchfrancF

F250,000Japaneseyen¥6,250,000SwissfrancSF62,500Euro62,500Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allr

ightsreservedCurrencyFuturesOptions⚫Areanoptiononacurrencyfuturescontract.⚫Exerciseofacurrencyfuturesoptionresultsinalongfuturesposition

fortheholderofacallorthewriterofaput.⚫Exerciseofacurrencyfuturesoptionresultsinashortfuturespositionforthesellerofacallorthebuyerofaput.

⚫Ifthefuturespositionisnotoffsetpriortoitsexpiration,foreigncurrencywillchangehands.Irwin/McGraw-HillCopyright©2

001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicOptionPricingRelationshipsatExpiry⚫Atexpiry,anAmericancalloptionisworthth

esameasaEuropeanoptionwiththesamecharacteristics.⚫Ifthecallisin-the-money,itisworthST–E.⚫Ifthecallisout-of-the-money,itisworthless.CaT=CeT=

Max[ST-E,0]Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicOptionPricingRelationshipsatExpiry⚫Ate

xpiry,anAmericanputoptionisworththesameasaEuropeanoptionwiththesamecharacteristics.⚫Iftheputisin-the-money,itisworthE-ST

.⚫Iftheputisout-of-the-money,itisworthless.PaT=PeT=Max[E-ST,0]Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,I

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

tsreservedBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossEE+CSTIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,I

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

llrightsreservedBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossESTE-pIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillComp

anies,Inc.AllrightsreservedAmericanOptionPricingRelationships⚫WithanAmericanoption,youcandoeverythingthat

youcandowithaEuropeanoption—thisoptiontoexerciseearlyhasvalue.CaT>CeT=Max[ST-E,0]PaT>PeT=Max[E-ST,0]Irwin/McGraw-HillCopyright©2001byTheMcGraw-Hil

lCompanies,Inc.AllrightsreservedMarketValue,TimeValueandIntrinsicValueforanAmericanCallCaT>Max[ST-E,0]ProfitlossESTMarketValueIntrinsicvalueTimeva

lueOut-of-the-moneyIn-the-moneyIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingRela

tionshipsConsidertwoinvestments1BuyacalloptionontheBritishpoundfuturescontract.Thecashflowtodayis-Ce2Replicatetheupsidepayoffofthecallby1Borr

owingthepresentvalueoftheexercisepriceofthecallintheU.S.ati$ThecashflowtodayisE/(1+i$)2LendingthepresentvalueofSTati£Thecashflowis

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

ricingRelationshipsWhentheoptionisin-the-moneybothstrategieshavethesamepayoff.Whentheoptionisout-of-the-moneyitha

sahigherpayofftheborrowingandlendingstrategy.Thus:0,)1()1(max$£+−+iEiSCTeIrwin/McGraw-HillCopy

right©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingRelationshipsUsingasimilarportfoliotoreplicatetheups

idepotentialofaput,wecanshowthat:0,)1()1(max£$+−+iSiEPTeIrwin/McGraw-HillCopyright©2001byTheMcGraw-

HillCompanies,Inc.AllrightsreservedBinomialOptionPricingModel⚫Imagineasimpleworldwherethedollar-euroexchangerateisS0($/)=$1todayandint

henextyear,S1($/)iseither$1.1or$.90.$1$.90$1.10S0($/)S1($/)Irwin/McGraw-HillCopyright©2001byTheMcGraw-Hill

Companies,Inc.AllrightsreservedBinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)⚫AcalloptionontheeurowithexercisepriceS0($/)=$1willha

vethefollowingpayoffs.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreserved$1$.90$1.

10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModel⚫Wecanreplicatethepayoffsofthecalloption.Withaleveredpositionintheeuro.Irwin/McG

raw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreserved$1$.90$1.10S0($/)S1($/)$.10$0C1($/)Binomial

OptionPricingModeldebt-$.90-$.90portfolio$.20$.00Borrowthepresentvalueof$.90todayandbuy1.Yournetpayoffin

oneperiodiseither$.2or$0.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBinomialOptionPricingModel$1$.90$

1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00⚫Theportfoliohastwicetheoption’spayoffsoth

eportfolioisworthtwicethecalloptionvalue.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allright

sreserved$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00BinomialOptionPricingModelTh

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

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

C1($/)debt-$.90-$.90portfolio$.20$.00Wecanvaluetheoptionashalfofthevalueoftheportfolio:+−=)1(90$.1$21$0iCIrwin/McGraw-HillCopyright©2001b

yTheMcGraw-HillCompanies,Inc.AllrightsreservedBinomialOptionPricingModel⚫Themostimportantlessonfromthebinomialoptionpr

icingmodelis:thereplicatingportfoliointuition.⚫Manyderivativesecuritiescanbevaluedbyvaluingportfoliosofprimitivesecuritiesw

henthoseportfolioshavethesamepayoffsasthederivativesecurities.Irwin/McGraw-HillCopyright©2001byTheMcGraw-Hi

llCompanies,Inc.AllrightsreservedEuropeanOptionPricingFormula⚫Wecanusethereplicatingportfoliointuitiondevel

opedinthebinomialoptionpricingformulatogenerateafaster-to-usemodelthataddressesamuchmorerealisticworld.Irwin/McGr

aw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingFormulaThemodelisTredNEdNFC$)]()([210−−=WhereC0=the

valueofaEuropeanoptionattimet=0TrrteSF)(£$−=r$=theinterestrateavailableintheU.S.r£=theinterestrateavailableintheforeigncountry

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

nPricingFormulaFindthevalueofasix-monthcalloptionontheBritishpoundwithanexercisepriceof$1.50=£1Thecurrentvalueofapoundis$1.60Theinterestrateavailab

leintheU.S.isr$=5%.TheinterestrateintheU.K.isr£=7%.Theoptionmaturityis6months(halfofayear).Thevolatilityofthe$/£exc

hangerateis30%p.a.Beforewestart,notethattheintrinsicvalueoftheoptionis$.10—ouranswermustbeatleastthat.Irwin/McGraw-HillCopyrig

ht©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingFormulaLet’stryourhandatusingthem

odel.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−=−=−=Tdd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=F106066.0

1=d176878.02−=dIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionValueDeterminantsCallP

ut1.Exchangerate+–2.Exerciseprice–+3.InterestrateinU.S.+–4.Interestrateinothercountry+–5.Variabilityinexchang

erate++6.Expirationdate++ThevalueofacalloptionC0mustfallwithinmax(S0–E,0)<C0<S0.Theprecisepositionwilldepen

dontheabovefactors.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEmpiricalTestsTheEuropeanoptionpricingmode

lworksfairlywellinpricingAmericancurrencyoptions.Itworksbestforout-of-the-moneyandat-the-moneyoptions.Whenoptionsare

in-the-money,theEuropeanoptionpricingmodeltendstounderpriceAmericanoptions.Irwin/McGraw-HillCopyright©2001byT

heMcGraw-HillCompanies,Inc.AllrightsreservedEndChapterNine