OptionsonForeignExchange(國(guó)際財(cái)務(wù)管理,英文版)課件

INTERNATIONALFINANCIALMANAGEMENTEUN/RESNICKSecondEdition9ChapterNineFuturesandOptions

onForeignExchangeChapterObjective:Thischapterdiscussesexchange-tradedcurrencyfuturescontracts,optionscontracts,andoptionsoncurrencyfutures.INTERNATIONALEUN/RESNICKSecoChapterOutlineFuturesContracts:PreliminariesCurrencyFuturesMarketsBasicCurrencyFuturesRelationshipsEurodollarInterestRateFuturesContractsOptionsContracts:PreliminariesCurrencyOptionsMarketsCurrencyFuturesOptionsChapterOutlineFuturesContracChapterOutline(continued)BasicOptionPricingRelationshipsatExpiryAmericanOptionPricingRelationshipsEuropeanOptionPricingRelationshipsBinomialOptionPricingModelEuropeanOptionPricingModelEmpiricalTestsofCurrencyOptionModelsChapterOutline(continued)BasFuturesContracts:PreliminariesAfuturescontractislikeaforwardcontract:Itspecifiesthatacertaincurrencywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.Afuturescontractisdifferentfromaforwardcontract:Futuresarestandardizedcontractstradingonorganizedexchangeswithdailyresettlementthroughaclearinghouse.FuturesContracts:PreliminariFuturesContracts:PreliminariesStandardizingFeatures:ContractSizeDeliveryMonthDailyresettlementInitialMargin(about4%ofcontractvalue,cashorT-billsheldinastreetnameatyourbrokers).FuturesContracts:PreliminariDailyResettlement:AnExampleSupposeyouwanttospeculateonariseinthe$/￥exchangerate(specificallyyouthinkthatthedollarwillappreciate).Currently$1=￥140.The3-monthforwardpriceis$1=￥150.DailyResettlement:AnExampleDailyResettlement:AnExampleCurrently$1=￥140anditappearsthatthedollarisstrengthening.Ifyouenterintoa3-monthfuturescontracttosell￥attherateof$1=￥150youwillmakemoneyiftheyendepreciates.Thecontractsizeis￥12,500,000Yourinitialmarginis4%ofthecontractvalue:

DailyResettlement:AnExampleDailyResettlement:AnExampleIftomorrow,thefuturesrateclosesat$1=￥149,thenyourposition’svaluedrops.Youroriginalagreementwastosell￥12,500,000andreceive$83,333.33Butnow￥12,500,000isworth$83,892.62Youhavelost$559.28overnight.DailyResettlement:AnExampleDailyResettlement:AnExampleThe$559.28comesoutofyour$3,333.33marginaccount,leaving$2,774.05Thisisshortofthe$3,355.70requiredforanewposition.Yourbrokerwillletyouslideuntilyourunthroughyourmaintenancemargin.Thenyoumustpostadditionalfundsoryourpositionwillbeclosedout.Thisisusuallydonewithareversingtrade.DailyResettlement:AnExampleCurrencyFuturesMarketsTheChicagoMercantileExchange(CME)isbyfarthelargest.Othersinclude:ThePhiladelphiaBoardofTrade(PBOT)TheMidAmericacommoditiesExchangeTheTokyoInternationalFinancialFuturesExchangeTheLondonInternationalFinancialFuturesExchangeCurrencyFuturesMarketsTheChTheChicagoMercantileExchangeExpirycycle:March,June,September,December.Deliverydate3rdWednesdayofdeliverymonth.Lasttradingdayisthesecondbusinessdayprecedingthedeliveryday.CMEhours7:20a.m.to2:00p.m.CST.TheChicagoMercantileExchangCMEAfterHoursExtended-hourstradingonGLOBEXrunsfrom2:30p.m.to4:00p.mdinnerbreakandthenbackatitfrom6:00p.m.to6:00a.m.CST.SingaporeInternationalMonetaryExchange(SIMEX)offerinterchangeablecontracts.There’sothermarkets,butnoneareclosetoCMEandSIMEXtradingvolume.CMEAfterHoursExtended-hoursBasicCurrency

FuturesRelationshipsOpenInterestreferstothenumberofcontractsoutstandingforaparticulardeliverymonth.Openinterestisagoodproxyfordemandforacontract.Somerefertoopeninterestasthedepthofthemarket.Thebreadthofthemarketwouldbehowmanydifferentcontracts(expirymonth,currency)areoutstanding.BasicCurrency

FuturesRelatiReadingaFuturesQuoteExpirymonthOpeningpriceHighestpricethatdayLowestpricethatdayClosingpriceDailyChangeHighestandlowestpricesoverthelifetimeofthecontract.NumberofopencontractsReadingaFuturesQuoteExpiry

EurodollarInterestRate

FuturesContracts

Widelyusedfuturescontractforhedgingshort-termU.S.dollarinterestraterisk.Theunderlyingassetisahypothetical$1,000,00090-dayEurodollardeposit—thecontractiscashsettled.TradedontheCMEandtheSingaporeInternationalMonetaryExchange.ThecontracttradesintheMarch,June,SeptemberandDecembercycle.

EurodollarInterestRate

FuReadingEurodollarFuturesQuotesEURODOLLAR(CME)—$1million;ptsof100%

OpenHighLowSettleChgYieldSettleChangeOpenInterestJuly94.6994.6994.6894.68-.015.32+.0147,417

Eurodollarfuturespricesarestatedasanindexnumberofthree-monthLIBORcalculatedasF=100-LIBOR.TheclosingpricefortheJulycontractis94.68thustheimpliedyieldis5.32percent=100–98.68Thechangewas.01percentof$1millionrepresenting$100onanannualbasis.Sinceitisa3-monthcontractonebasispointcorrespondstoa$25pricechange.ReadingEurodollarFuturesQuoOptionsContracts:PreliminariesAnoptiongivestheholdertheright,butnottheobligation,tobuyorsellagivenquantityofanassetinthefuture,atpricesagreedupontoday.Callsvs.PutsCalloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.OptionsContracts:PreliminariOptionsContracts:PreliminariesEuropeanvs.AmericanoptionsEuropeanoptionscanonlybeexercisedontheexpirationdate.Americanoptionscanbeexercisedatanytimeuptoandincludingtheexpirationdate.Sincethisoptiontoexerciseearlygenerallyhasvalue,AmericanoptionsareusuallyworthmorethanEuropeanoptions,otherthingsequal.OptionsContracts:PreliminariOptionsContracts:PreliminariesIn-the-moneyTheexercisepriceislessthanthespotpriceoftheunderlyingasset.At-the-moneyTheexercisepriceisequaltothespotpriceoftheunderlyingasset.Out-of-the-moneyTheexercisepriceismorethanthespotpriceoftheunderlyingasset.OptionsContracts:PreliminariOptionsContracts:PreliminariesIntrinsicValueThedifferencebetweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.SpeculativeValueThedifferencebetweentheoptionpremiumandtheintrinsicvalueoftheoption.OptionPremium=IntrinsicValueSpeculativeValue+OptionsContracts:PreliminariCurrencyOptionsMarketsPHLXHKFE20-hourtradingday.OTCvolumeismuchbiggerthanexchangevolume.TradingisinsevenmajorcurrenciesplustheeuroagainsttheU.S.dollar.CurrencyOptionsMarketsPHLXPHLXCurrencyOptionSpecifications62,500PHLXCurrencyOptionSpecificaCurrencyFuturesOptionsAreanoptiononacurrencyfuturescontract.Exerciseofacurrencyfuturesoptionresultsinalongfuturespositionfortheholderofacallorthewriterofaput.Exerciseofacurrencyfuturesoptionresultsinashortfuturespositionforthesellerofacallorthebuyerofaput.Ifthefuturespositionisnotoffsetpriortoitsexpiration,foreigncurrencywillchangehands.CurrencyFuturesOptionsAreanBasicOptionPricing

RelationshipsatExpiryAtexpiry,anAmericancalloptionisworththesameasaEuropeanoptionwiththesamecharacteristics.Ifthecallisin-the-money,itisworthST–E.Ifthecallisout-of-the-money,itisworthless.CaT=CeT

=Max[ST-E,0]BasicOptionPricing

RelationBasicOptionPricing

RelationshipsatExpiryAtexpiry,anAmericanputoptionisworththesameasaEuropeanoptionwiththesamecharacteristics.Iftheputisin-the-money,itisworthE-ST.Iftheputisout-of-the-money,itisworthless.PaT=PeT

=Max[E-ST,0]BasicOptionPricing

RelationBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossEE+CSTLong1callBasicOptionProfitProfilesCaBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossEE+CSTshort1callBasicOptionProfitProfilesCaBasicOptionProfitProfilesPaT=PeT=Max[E-ST,0]profitlossEE-pSTlong1putBasicOptionProfitProfilesPaBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossESTShort1putE-pBasicOptionProfitProfilesCaAmericanOptionPricingRelationshipsWithanAmericanoption,youcandoeverythingthatyoucandowithaEuropeanoption—thisoptiontoexerciseearlyhasvalue.CaT

>

CeT=Max[ST-E,0]PaT

>

PeT=Max[E-ST,0]AmericanOptionPricingRelatiMarketValue,TimeValueandIntrinsicValueforanAmericanCallCaT

>Max[ST-E,0]ProfitlossESTMarketValueIntrinsicvalueST-ETimevalueOut-of-the-moneyIn-the-moneyMarketValue,TimeValueandIEuropeanOptionPricingRelationshipsConsidertwoinvestmentsBuyacalloptionontheBritishpoundfuturescontract.Thecashflowtodayis-CeReplicatetheupsidepayoffofthecallbyBorrowingthepresentvalueoftheexercisepriceofthecallintheU.S.ati$Thecashflowtodayis E/(1+i$)LendingthepresentvalueofSTati￡Thecashflowis -ST/(1+i￡)EuropeanOptionPricingRelatiEuropeanOptionPricingRelationshipsWhentheoptionisin-the-moneybothstrategieshavethesamepayoff.Whentheoptionisout-of-the-moneyithasahigherpayofftheborrowingandlendingstrategy.Thus:EuropeanOptionPricingRelatiEuropeanOptionPricingRelationshipsUsingasimilarportfoliotoreplicatetheupsidepotentialofaput,wecanshowthat:EuropeanOptionPricingRelatiBinomialOptionPricingModelImagineasimpleworldwherethedollar-euroexchangerateisS0($/)=$1todayandinthenextyear,S1($/)iseither$1.1or$.90.$1$.90$1.10S0($/)S1($/)BinomialOptionPricingModelIBinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)Acalloptionontheeurowithexerciseprice

S0($/)=$1willhavethefollowingpayoffs.BinomialOptionPricingModel$$1$.90$1.10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModelWecanreplicatethepayoffsofthecalloption.Withaleveredpositionintheeuro.$1$.90$1.10S0($/)S1($/)$.1$1$.90$1.10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModeldebt-$.90-$.90portfolio$.20$.00Borrowthepresentvalueof$.90todayandbuy1.Yournetpayoffinoneperiodiseither$.2or$0.$1$.90$1.10S0($/)S1($/)$.1BinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00Theportfoliohastwicetheoption’spayoffsotheportfolioisworthtwicethecalloptionvalue.BinomialOptionPricingModel$$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00BinomialOptionPricingModel

Theportfoliovaluetodayistoday’svalueofoneeurolessthepresentvalueofa$.90debt:$1$.90$1.10S0($/)S1($/)$.1BinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00Wecanvaluetheoptionashalfofthevalueoftheportfolio:BinomialOptionPricingModel$BinomialOptionPricingModelThemostimportantlessonfromthebinomialoptionpricingmodelis:thereplicatingportfoliointuition.Manyderivativesecuritiescanbevaluedbyvaluingportfoliosofprimitivesecuritieswhenthoseportfolioshavethesamepayoffsasthederivativesecurities.BinomialOptionPricingModelTEuropeanOptionPricingFormulaWecanusethereplicatingportfoliointuitiondevelopedinthebinomialoptionpricingformulatogenerateafaster-to-usemodelthataddressesamuchmorerealisticworld.EuropeanOptionPricingFormulEuropeanOptionPricingFormulaThemodelisWhereC0=thevalueofaEuropeanoptionattimet=0r$=theinterestrateavailableintheU.S.r￡=theinterestrateavailableintheforeigncountry—inthiscasetheU.K.EuropeanOptionPricingFormulEuropeanOptionPricingFormulaFindthevalueofasix-monthcalloptionontheBritishpoundwithanexercisepriceof$1.50=￡1Thecurrentvalueofapoundis$1.60TheinterestrateavailableintheU.S.isr$=5%.TheinterestrateintheU.K.isr￡=7%.Theoptionmaturityis6months(halfofayear).Thevolatilityofthe$/￡exchangerateis30%p.a.Beforewestart,notethattheintrinsicvalueoftheoptionis$.10—ouranswermustbeatleastthat.EuropeanOptionPricingFormulEuropeanOptionPricingFormulaLet’stryourhandatusingthemodel.Ifyouhaveacalculatorhandy,followalong.Then,calculated1andd2FirstcalculateEuropeanOptionPricingFormulEuropeanOptionPricingFormulaN(d1)=N(0.106066)=.5422N(d2)=N(-0.1768)=0.4298EuropeanOptionPricingFormulOptionValueDeterminants Call Put

1. Exchangerate + –

2. Exerciseprice – +

3. InterestrateinU.S. + –

4. Interestrateinothercountry + –

5. Variabilityinexchangerate + +

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

C0

<

S0.

Theprecisepositionwilldependontheabovefactors.OptionValueDeterminants EmpiricalTestsTheEuropeanoptionpricingmodelworksfairlywellinpricingAmericancurrencyoptions.Itworksbestforout-of-the-moneyandat-the-moneyoptions.Whenoptionsarein-the-money,theEuropeanoptionpricingmodeltendstounderpriceAmericanoptions.EmpiricalTestsTheEuropeanopEndChapterNineEndChapterNineINTERNATIONALFINANCIALMANAGEMENTEUN/RESNICKSecondEdition9ChapterNineFuturesandOptions

onForeignExchangeChapterObjective:Thischapterdiscussesexchange-tradedcurrencyfuturescontracts,optionscontracts,andoptionsoncurrencyfutures.INTERNATIONALEUN/RESNICKSecoChapterOutlineFuturesContracts:PreliminariesCurrencyFuturesMarketsBasicCurrencyFuturesRelationshipsEurodollarInterestRateFuturesContractsOptionsContracts:PreliminariesCurrencyOptionsMarketsCurrencyFuturesOptionsChapterOutlineFuturesContracChapterOutline(continued)BasicOptionPricingRelationshipsatExpiryAmericanOptionPricingRelationshipsEuropeanOptionPricingRelationshipsBinomialOptionPricingModelEuropeanOptionPricingModelEmpiricalTestsofCurrencyOptionModelsChapterOutline(continued)BasFuturesContracts:PreliminariesAfuturescontractislikeaforwardcontract:Itspecifiesthatacertaincurrencywillbeexchangedforanotherataspecifiedtimeinthefutureatpricesspecifiedtoday.Afuturescontractisdifferentfromaforwardcontract:Futuresarestandardizedcontractstradingonorganizedexchangeswithdailyresettlementthroughaclearinghouse.FuturesContracts:PreliminariFuturesContracts:PreliminariesStandardizingFeatures:ContractSizeDeliveryMonthDailyresettlementInitialMargin(about4%ofcontractvalue,cashorT-billsheldinastreetnameatyourbrokers).FuturesContracts:PreliminariDailyResettlement:AnExampleSupposeyouwanttospeculateonariseinthe$/￥exchangerate(specificallyyouthinkthatthedollarwillappreciate).Currently$1=￥140.The3-monthforwardpriceis$1=￥150.DailyResettlement:AnExampleDailyResettlement:AnExampleCurrently$1=￥140anditappearsthatthedollarisstrengthening.Ifyouenterintoa3-monthfuturescontracttosell￥attherateof$1=￥150youwillmakemoneyiftheyendepreciates.Thecontractsizeis￥12,500,000Yourinitialmarginis4%ofthecontractvalue:

DailyResettlement:AnExampleDailyResettlement:AnExampleIftomorrow,thefuturesrateclosesat$1=￥149,thenyourposition’svaluedrops.Youroriginalagreementwastosell￥12,500,000andreceive$83,333.33Butnow￥12,500,000isworth$83,892.62Youhavelost$559.28overnight.DailyResettlement:AnExampleDailyResettlement:AnExampleThe$559.28comesoutofyour$3,333.33marginaccount,leaving$2,774.05Thisisshortofthe$3,355.70requiredforanewposition.Yourbrokerwillletyouslideuntilyourunthroughyourmaintenancemargin.Thenyoumustpostadditionalfundsoryourpositionwillbeclosedout.Thisisusuallydonewithareversingtrade.DailyResettlement:AnExampleCurrencyFuturesMarketsTheChicagoMercantileExchange(CME)isbyfarthelargest.Othersinclude:ThePhiladelphiaBoardofTrade(PBOT)TheMidAmericacommoditiesExchangeTheTokyoInternationalFinancialFuturesExchangeTheLondonInternationalFinancialFuturesExchangeCurrencyFuturesMarketsTheChTheChicagoMercantileExchangeExpirycycle:March,June,September,December.Deliverydate3rdWednesdayofdeliverymonth.Lasttradingdayisthesecondbusinessdayprecedingthedeliveryday.CMEhours7:20a.m.to2:00p.m.CST.TheChicagoMercantileExchangCMEAfterHoursExtended-hourstradingonGLOBEXrunsfrom2:30p.m.to4:00p.mdinnerbreakandthenbackatitfrom6:00p.m.to6:00a.m.CST.SingaporeInternationalMonetaryExchange(SIMEX)offerinterchangeablecontracts.There’sothermarkets,butnoneareclosetoCMEandSIMEXtradingvolume.CMEAfterHoursExtended-hoursBasicCurrency

FuturesRelationshipsOpenInterestreferstothenumberofcontractsoutstandingforaparticulardeliverymonth.Openinterestisagoodproxyfordemandforacontract.Somerefertoopeninterestasthedepthofthemarket.Thebreadthofthemarketwouldbehowmanydifferentcontracts(expirymonth,currency)areoutstanding.BasicCurrency

FuturesRelatiReadingaFuturesQuoteExpirymonthOpeningpriceHighestpricethatdayLowestpricethatdayClosingpriceDailyChangeHighestandlowestpricesoverthelifetimeofthecontract.NumberofopencontractsReadingaFuturesQuoteExpiry

EurodollarInterestRate

FuturesContracts

Widelyusedfuturescontractforhedgingshort-termU.S.dollarinterestraterisk.Theunderlyingassetisahypothetical$1,000,00090-dayEurodollardeposit—thecontractiscashsettled.TradedontheCMEandtheSingaporeInternationalMonetaryExchange.ThecontracttradesintheMarch,June,SeptemberandDecembercycle.

EurodollarInterestRate

FuReadingEurodollarFuturesQuotesEURODOLLAR(CME)—$1million;ptsof100%

OpenHighLowSettleChgYieldSettleChangeOpenInterestJuly94.6994.6994.6894.68-.015.32+.0147,417

Eurodollarfuturespricesarestatedasanindexnumberofthree-monthLIBORcalculatedasF=100-LIBOR.TheclosingpricefortheJulycontractis94.68thustheimpliedyieldis5.32percent=100–98.68Thechangewas.01percentof$1millionrepresenting$100onanannualbasis.Sinceitisa3-monthcontractonebasispointcorrespondstoa$25pricechange.ReadingEurodollarFuturesQuoOptionsContracts:PreliminariesAnoptiongivestheholdertheright,butnottheobligation,tobuyorsellagivenquantityofanassetinthefuture,atpricesagreedupontoday.Callsvs.PutsCalloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.OptionsContracts:PreliminariOptionsContracts:PreliminariesEuropeanvs.AmericanoptionsEuropeanoptionscanonlybeexercisedontheexpirationdate.Americanoptionscanbeexercisedatanytimeuptoandincludingtheexpirationdate.Sincethisoptiontoexerciseearlygenerallyhasvalue,AmericanoptionsareusuallyworthmorethanEuropeanoptions,otherthingsequal.OptionsContracts:PreliminariOptionsContracts:PreliminariesIn-the-moneyTheexercisepriceislessthanthespotpriceoftheunderlyingasset.At-the-moneyTheexercisepriceisequaltothespotpriceoftheunderlyingasset.Out-of-the-moneyTheexercisepriceismorethanthespotpriceoftheunderlyingasset.OptionsContracts:PreliminariOptionsContracts:PreliminariesIntrinsicValueThedifferencebetweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.SpeculativeValueThedifferencebetweentheoptionpremiumandtheintrinsicvalueoftheoption.OptionPremium=IntrinsicValueSpeculativeValue+OptionsContracts:PreliminariCurrencyOptionsMarketsPHLXHKFE20-hourtradingday.OTCvolumeismuchbiggerthanexchangevolume.TradingisinsevenmajorcurrenciesplustheeuroagainsttheU.S.dollar.CurrencyOptionsMarketsPHLXPHLXCurrencyOptionSpecifications62,500PHLXCurrencyOptionSpecificaCurrencyFuturesOptionsAreanoptiononacurrencyfuturescontract.Exerciseofacurrencyfuturesoptionresultsinalongfuturespositionfortheholderofacallorthewriterofaput.Exerciseofacurrencyfuturesoptionresultsinashortfuturespositionforthesellerofacallorthebuyerofaput.Ifthefuturespositionisnotoffsetpriortoitsexpiration,foreigncurrencywillchangehands.CurrencyFuturesOptionsAreanBasicOptionPricing

RelationshipsatExpiryAtexpiry,anAmericancalloptionisworththesameasaEuropeanoptionwiththesamecharacteristics.Ifthecallisin-the-money,itisworthST–E.Ifthecallisout-of-the-money,itisworthless.CaT=CeT

=Max[ST-E,0]BasicOptionPricing

RelationBasicOptionPricing

RelationshipsatExpiryAtexpiry,anAmericanputoptionisworththesameasaEuropeanoptionwiththesamecharacteristics.Iftheputisin-the-money,itisworthE-ST.Iftheputisout-of-the-money,itisworthless.PaT=PeT

=Max[E-ST,0]BasicOptionPricing

RelationBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossEE+CSTLong1callBasicOptionProfitProfilesCaBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossEE+CSTshort1callBasicOptionProfitProfilesCaBasicOptionProfitProfilesPaT=PeT=Max[E-ST,0]profitlossEE-pSTlong1putBasicOptionProfitProfilesPaBasicOptionProfitProfilesCaT=CeT=Max[ST-E,0]profitlossESTShort1putE-pBasicOptionProfitProfilesCaAmericanOptionPricingRelationshipsWithanAmericanoption,youcandoeverythingthatyoucandowithaEuropeanoption—thisoptiontoexerciseearlyhasvalue.CaT

>

CeT=Max[ST-E,0]PaT

>

PeT=Max[E-ST,0]AmericanOptionPricingRelatiMarketValue,TimeValueandIntrinsicValueforanAmericanCallCaT

>Max[ST-E,0]ProfitlossESTMarketValueIntrinsicvalueST-ETimevalueOut-of-the-moneyIn-the-moneyMarketValue,TimeValueandIEuropeanOptionPricingRelationshipsConsidertwoinvestmentsBuyacalloptionontheBritishpoundfuturescontract.Thecashflowtodayis-CeReplicatetheupsidepayoffofthecallbyBorrowingthepresentvalueoftheexercisepriceofthecallintheU.S.ati$Thecashflowtodayis E/(1+i$)LendingthepresentvalueofSTati￡Thecashflowis -ST/(1+i￡)EuropeanOptionPricingRelatiEuropeanOptionPricingRelationshipsWhentheoptionisin-the-moneybothstrategieshavethesamepayoff.Whentheoptionisout-of-the-moneyithasahigherpayofftheborrowingandlendingstrategy.Thus:EuropeanOptionPricingRelatiEuropeanOptionPricingRelationshipsUsingasimilarportfoliotoreplicatetheupsidepotentialofaput,wecanshowthat:EuropeanOptionPricingRelatiBinomialOptionPricingModelImagineasimpleworldwherethedollar-euroexchangerateisS0($/)=$1todayandinthenextyear,S1($/)iseither$1.1or$.90.$1$.90$1.10S0($/)S1($/)BinomialOptionPricingModelIBinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)Acalloptionontheeurowithexerciseprice

S0($/)=$1willhavethefollowingpayoffs.BinomialOptionPricingModel$$1$.90$1.10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModelWecanreplicatethepayoffsofthecalloption.Withaleveredpositionintheeuro.$1$.90$1.10S0($/)S1($/)$.1$1$.90$1.10S0($/)S1($/)$.10$0C1($/)BinomialOptionPricingModeldebt-$.90-$.90portfolio$.20$.00Borrowthepresentvalueof$.90todayandbuy1.Yournetpayoffinoneperiodiseither$.2or$0.$1$.90$1.10S0($/)S1($/)$.1BinomialOptionPricingModel$1$.90$1.10S0($/)S1($/)$.10$0C1($/)debt-$.90-$.90portfolio$.20$.00Theportfoliohastwicetheoption’spayoffsotheportfolioisworthtwicethecalloptionvalue.BinomialOptionPricingModel$$1$.90$1.10S0($/)S1($/)$.10$0C1($/)