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Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedINTERNATIONALFINANCIALMANAGEMENTEUN/RESNICKSecondEdition9Cha

pterNineFuturesandOptionsonForeignExchangeChapterObjective:Thischapterdiscussesexchange-tradedcurren

cyfuturescontracts,optionscontracts,andoptionsoncurrencyfutures.Irwin/McGraw-HillCopyright©2001byTheMcGraw-Hil

lCompanies,Inc.AllrightsreservedChapterOutline⚫FuturesContracts:Preliminaries⚫CurrencyFuturesMarkets⚫Basi

cCurrencyFuturesRelationships⚫EurodollarInterestRateFuturesContracts⚫OptionsContracts:Preliminaries⚫Curre

ncyOptionsMarkets⚫CurrencyFuturesOptionsIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedChapterOutline(continued)⚫

BasicOptionPricingRelationshipsatExpiry⚫AmericanOptionPricingRelationships⚫EuropeanOptionPricingRelations

hips⚫BinomialOptionPricingModel⚫EuropeanOptionPricingModel⚫EmpiricalTestsofCurrencyOptionModelsIrwin/McGraw-Hil

lCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedFuturesContracts:Preliminaries⚫Afuturescontr

actislikeaforwardcontract:◼Itspecifiesthatacertaincurrencywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.⚫Afuture

scontractisdifferentfromaforwardcontract:◼Futuresarestandardizedcontractstradingonorganizedexchangeswithdailyreset

tlementthroughaclearinghouse.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedFuturesContracts

:Preliminaries⚫StandardizingFeatures:◼ContractSize◼DeliveryMonth◼Dailyresettlement⚫InitialMargin(about4%ofcontractvalue,cashorT-bill

sheldinastreetnameatyourbrokers).Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExample⚫Suppo

seyouwanttospeculateonariseinthe$/¥exchangerate(specificallyyouthinkthatthedollarwillappreciate).Currently$1=¥140.The3-monthforwa

rdpriceis$1=¥150.CurrencyperU.S.$equivalentU.S.$WedTueWedTueJapan(yen)0.0071428570.0071942451401391-monthforward0.0069930070.00704225414

31423-monthsforward0.0066666670.0067114091501496-monthsforward0.006250.006289308160159Irwin/McGraw-HillCopyright©2001byTheMc

Graw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExample⚫Currently$1=¥140anditappearsthatthedollarisstrengthening.⚫Ifyouenter

intoa3-monthfuturescontracttosell¥attherateof$1=¥150youwillmakemoneyiftheyendepreciates.Thecontracts

izeis¥12,500,000⚫Yourinitialmarginis4%ofthecontractvalue:?50$10?2,500,00.04$3,333.33=Irwin/McGraw-HillCopyri

ght©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedDailyResettlement:AnExampleIftomorrow,thefuturesratecl

osesat$1=¥149,thenyourposition’svaluedrops.Youroriginalagreementwastosell¥12,500,000andreceive$83,333.33Butnow¥12,500,000isworth$83,892.62?4

9$10?2,500,0062.892,83$=Youhavelost$559.28overnight.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCo

mpanies,Inc.AllrightsreservedDailyResettlement:AnExample⚫The$559.28comesoutofyour$3,333.33marginaccount,leavin

g$2,774.05⚫Thisisshortofthe$3,355.70requiredforanewposition.?49$10?2,500,00.04$3,355.70=⚫Yourbrokerwi

llletyouslideuntilyourunthroughyourmaintenancemargin.Thenyoumustpostadditionalfundsoryourpositionwillbeclosedout.Thi

sisusuallydonewithareversingtrade.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedCur

rencyFuturesMarkets⚫TheChicagoMercantileExchange(CME)isbyfarthelargest.⚫Othersinclude:◼ThePhiladelphiaBoa

rdofTrade(PBOT)◼TheMidAmericacommoditiesExchange◼TheTokyoInternationalFinancialFuturesExchange◼TheLondonInternationalF

inancialFuturesExchangeIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedTheChicagoMercantileExchange⚫Expirycyc

le:March,June,September,December.⚫Deliverydate3rdWednesdayofdeliverymonth.⚫Lasttradingdayisthesecondbusinessdayprecedingthedeliver

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

rvedCMEAfterHours⚫Extended-hourstradingonGLOBEXrunsfrom2:30p.m.to4:00p.mdinnerbreakandthenbackatitfrom6:0

0p.m.to6:00a.m.CST.⚫SingaporeInternationalMonetaryExchange(SIMEX)offerinterchangeablecontracts.⚫There’sothermark

ets,butnoneareclosetoCMEandSIMEXtradingvolume.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicCurrencyFutur

esRelationships⚫OpenInterestreferstothenumberofcontractsoutstandingforaparticulardeliverymonth.⚫Openinterestisagoodpr

oxyfordemandforacontract.⚫Somerefertoopeninterestasthedepthofthemarket.Thebreadthofthemarketwouldbehowman

ydifferentcontracts(expirymonth,currency)areoutstanding.Irwin/McGraw-HillCopyright©2001byTheMcGraw-Hil

lCompanies,Inc.AllrightsreservedReadingaFuturesQuoteOpenHiLoSettleChangeLifetimeHighLifetimeLowOpenInterestSept.9282.9325.9276.93

09+.00271.2085.863674,639ExpirymonthOpeningpriceHighestpricethatdayLowestpricethatdayClosingpriceDailyChangeHighestan

dlowestpricesoverthelifetimeofthecontract.NumberofopencontractsIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreserv

edEurodollarInterestRateFuturesContracts⚫Widelyusedfuturescontractforhedgingshort-termU.S.dollarinterestraterisk.⚫Theu

nderlyingassetisahypothetical$1,000,00090-dayEurodollardeposit—thecontractiscashsettled.⚫TradedontheCMEa

ndtheSingaporeInternationalMonetaryExchange.⚫ThecontracttradesintheMarch,June,SeptemberandDecembercycle.Irw

in/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedReadingEurodollarFuturesQuot

esEURODOLLAR(CME)—$1million;ptsof100%OpenHighLowSettleChgYieldSettleChangeOpenInterestJuly94.6994.6994.6894.68-.015.32+.01

47,417Eurodollarfuturespricesarestatedasanindexnumberofthree-monthLIBORcalculatedasF=100-LIBOR.TheclosingpricefortheJulycontrac

tis94.68thustheimpliedyieldis5.32percent=100–98.68Thechangewas.01percentof$1millionrepresenting$100on

anannualbasis.Sinceitisa3-monthcontractonebasispointcorrespondstoa$25pricechange.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanie

s,Inc.AllrightsreservedOptionsContracts:Preliminaries⚫Anoptiongivestheholdertheright,butnottheobligation,tobuyorsellagivenquantityofanassetinthef

uture,atpricesagreedupontoday.⚫Callsvs.Puts◼Calloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimei

nthefuture,atpricesagreedupontoday.◼Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofsomeassetatsometim

einthefuture,atpricesagreedupontoday.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionsContracts:Prelimina

ries⚫Europeanvs.Americanoptions◼Europeanoptionscanonlybeexercisedontheexpirationdate.◼Americanoptionscanbeexercisedatanyt

imeuptoandincludingtheexpirationdate.◼Sincethisoptiontoexerciseearlygenerallyhasvalue,AmericanoptionsareusuallyworthmorethanEurop

eanoptions,otherthingsequal.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptio

nsContracts:Preliminaries⚫In-the-money◼Theexercisepriceislessthanthespotpriceoftheunderlyingasset.⚫At-the-money◼Theexercisepriceisequaltothespo

tpriceoftheunderlyingasset.⚫Out-of-the-money◼Theexercisepriceismorethanthespotpriceoftheunderlyingasset.Irwin/McGraw-

HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionsContracts:Preliminaries⚫IntrinsicValue◼Thedifferencebe

tweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.⚫SpeculativeValue◼Thedifferencebetweentheoptionpremiumandtheintrinsicvalu

eoftheoption.OptionPremium=IntrinsicValueSpeculativeValue+Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedCurrency

OptionsMarkets⚫PHLX⚫HKFE⚫20-hourtradingday.⚫OTCvolumeismuchbiggerthanexchangevolume.⚫Tradingisinsevenmajorcurrencie

splustheeuroagainsttheU.S.dollar.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedPHLXCurrencyO

ptionSpecificationsCurrencyContractSizeAustraliandollarAD50,000Britishpound£31,250CanadiandollarCD50,000DeutschemarkDM62,500Fren

chfrancFF250,000Japaneseyen¥6,250,000SwissfrancSF62,500Euro62,500Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillC

ompanies,Inc.AllrightsreservedCurrencyFuturesOptions⚫Areanoptiononacurrencyfuturescontract.⚫Exerciseofacurrencyfuturesoptionresultsinalongfu

turespositionfortheholderofacallorthewriterofaput.⚫Exerciseofacurrencyfuturesoptionresultsinashortfuturespositionforthesellerofacallorthebuyerofaput

.⚫Ifthefuturespositionisnotoffsetpriortoitsexpiration,foreigncurrencywillchangehands.Irwin/McGraw-HillCopyright©2001byTheMc

Graw-HillCompanies,Inc.AllrightsreservedBasicOptionPricingRelationshipsatExpiry⚫Atexpiry,anAmericancalloptionisworththesameasaEuropeanoption

withthesamecharacteristics.⚫Ifthecallisin-the-money,itisworthST–E.⚫Ifthecallisout-of-the-money,itisworthless.CaT=CeT=Max[ST-E,0]Irwin/McGraw-

HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBasicOptionPricingRelationshipsatExpiry⚫Atexpiry,anAmericanputoptionisworththe

sameasaEuropeanoptionwiththesamecharacteristics.⚫Iftheputisin-the-money,itisworthE-ST.⚫Iftheputisout-

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

servedBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossEE+CSTIrwin/McGraw-HillCopyright©2001byT

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

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

raw-HillCompanies,Inc.AllrightsreservedBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossESTE-pIrwin/McGraw-HillCopy

right©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedAmericanOptionPricingRelationships⚫WithanAmericanopti

on,youcandoeverythingthatyoucandowithaEuropeanoption—thisoptiontoexerciseearlyhasvalue.CaT>CeT=Max[ST-E,0]PaT>PeT=Max[E-ST,0]Irwin/McGraw-H

illCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedMarketValue,TimeValueandIntrinsicValueforanAmericanCallCaT>

Max[ST-E,0]ProfitlossESTMarketValueIntrinsicvalueTimevalueOut-of-the-moneyIn-the-moneyIrwin/McGraw-HillCop

yright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingRelationshipsConsidertwoinvestments1Buyacal

loptionontheBritishpoundfuturescontract.Thecashflowtodayis-Ce2Replicatetheupsidepayoffofthecallby1Borrowingthepresentvalueoftheexercisepriceofthe

callintheU.S.ati$ThecashflowtodayisE/(1+i$)2LendingthepresentvalueofSTati£Thecashflowis-ST/(1+i£)Irwin/McGraw-HillCopyright©2001byT

heMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingRelationshipsWhentheoptionisin-the-moneybothstrategieshavethesamepayo

ff.Whentheoptionisout-of-the-moneyithasahigherpayofftheborrowingandlendingstrategy.Thus:0,)1()1(max$£+−+iEiSCTeIrwin/McGraw-HillCo

pyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingRelationshipsUsingasimilarportfoliotoreplicatetheup

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

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

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

nies,Inc.AllrightsreservedBinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)⚫Acalloptionontheeurow

ithexercisepriceS0($/)=$1willhavethefollowingpayoffs.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreserved$1$.

90$1.10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModel⚫Wecanreplicatethepayoffsofthecalloption.Withaleveredpositioninthee

uro.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreserved$1$.90$1.10S0($/)S

1($/)$.10$0C1($/)BinomialOptionPricingModeldebt-$.90-$.90portfolio$.20$.00Borrowthepresentvalueof$.90todayandbuy1.Yournetpayoffinoneper

iodiseither$.2or$0.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedBinomial

OptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00⚫Theportfoliohastwicetheoption’spayoffsotheportfolioisworthtw

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

($/)debt-$.90-$.90portfolio$.20$.00BinomialOptionPricingModelTheportfoliovaluetodayistoday’svalueofonee

urolessthepresentvalueofa$.90debt:)1(90$.1$$i+−Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrig

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

ashalfofthevalueoftheportfolio:+−=)1(90$.1$21$0iCIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompan

ies,Inc.AllrightsreservedBinomialOptionPricingModel⚫Themostimportantlessonfromthebinomialoptionpricingmodelis:there

plicatingportfoliointuition.⚫Manyderivativesecuritiescanbevaluedbyvaluingportfoliosofprimitivesecuritieswhenthoseportfolioshavethesamep

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

rvedEuropeanOptionPricingFormula⚫Wecanusethereplicatingportfoliointuitiondevelopedinthebinomialoptionpricingformulatogenerateafaster

-to-usemodelthataddressesamuchmorerealisticworld.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrightsreserved

EuropeanOptionPricingFormulaThemodelisTredNEdNFC$)]()([210−−=WhereC0=thevalueofaEuropeanoptionattimet=0TrrteSF)(

£$−=r$=theinterestrateavailableintheU.S.r£=theinterestrateavailableintheforeigncountry—inthiscasetheU

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

cingFormulaFindthevalueofasix-monthcalloptionontheBritishpoundwithanexercisepriceof$1.50=£1Thecurrentvalueofapoundis

$1.60TheinterestrateavailableintheU.S.isr$=5%.TheinterestrateintheU.K.isr£=7%.Theoptionmaturityis6mont

hs(halfofayear).Thevolatilityofthe$/£exchangerateis30%p.a.Beforewestart,notethattheintrinsicvalueoftheoptionis$.10—ouranswermustbeatleastthat.Irw

in/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEuropeanOptionPricingFormulaLet’stryourhandatusingthem

odel.Ifyouhaveacalculatorhandy,followalong.Then,calculated1andd2106066.05.4.5.)4.0(5.)50.1/485075.1ln(5.)/ln(221=+=+=TTEFdFirstcalculate4850

75.150.150.0)07.05(.)(£$===−−eeSFTrrt176878.05.4.106066.012−=−=−=TddIrwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrigh

tsreservedEuropeanOptionPricingFormulaN(d1)=N(0.106066)=.5422N(d2)=N(-0.1768)=0.4298TredNEdNFC$)]()([21

0−−=157.0$]4298.50.15422.485075.1[5.*05.0=−=−eC485075.1=F106066.01=d176878.02−=dIrwin/McGraw-HillCopyright©2001

byTheMcGraw-HillCompanies,Inc.AllrightsreservedOptionValueDeterminantsCallPut1.Exchangerate+–2.Exerci

seprice–+3.InterestrateinU.S.+–4.Interestrateinothercountry+–5.Variabilityinexchangerate++6.Expirationdate++ThevalueofacalloptionC

0mustfallwithinmax(S0–E,0)<C0<S0.Theprecisepositionwilldependontheabovefactors.Irwin/McGraw-HillCopyright

©2001byTheMcGraw-HillCompanies,Inc.AllrightsreservedEmpiricalTestsTheEuropeanoptionpricingmodelworksfa

irlywellinpricingAmericancurrencyoptions.Itworksbestforout-of-the-moneyandat-the-moneyoptions.Whenoptionsarein-th

e-money,theEuropeanoptionpricingmodeltendstounderpriceAmericanoptions.Irwin/McGraw-HillCopyright©2001byTheMcGraw-HillCompanies,Inc.Allrig

htsreservedEndChapterNine