FuturesandOptionsonForeignExchangeChapter7Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.ChapterOutlineFuturesContracts:SomePreliminariesCurrencyFuturesMarketsBasicCurrencyFuturesRelationshipsOptionsContracts:SomePreliminariesCurrencyOptionsMarketsCurrencyFuturesOptionsBasicOption-PricingRelationshipsatExpirationAmericanOption-PricingRelationshipsEuropeanOption-PricingRelationshipsBinomialOption-PricingModelEuropeanOption-PricingModelEmpiricalTestsofCurrencyOptionsSummary7-2Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.FuturesContracts:PreliminariesBothforwardandfuturescontractsarederivativeorcontingentclaimsecuritiesbecausetheirvaluesarederivedfromorcontingentuponthevalueoftheunderlyingsecurityForwardcontractTailor-madeforaclientbytheirinternationalbankFuturescontractStandardizedfeatures(e.g.,contractsize,maturitydate,deliverymonths)Exchangetraded7-3Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.FuturesContracts:Preliminaries(Continued)Aninitialperformancebond(formerlycalledmargin)mustbedepositedintoacollateralaccounttoestablishafuturespositionGenerallyequalto2%ofcontractvalueCashorT-billsmaybeusedtomeetrequirementMajordifferencebetweenforwardcontractandfuturescontractisthewaytheunderlyingassetispricedforfuturepurchaseorsaleForwardcontractstatesapriceforthefuturetransaction,butfuturescontractissettled-up,ormarked-to-market,dailyatthesettlementprice7-4Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.DifferencesbetweenFuturesandForwardContract7-5Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.CurrencyFuturesMarketsTradingincurrencyfuturesbeganattheChicagoMercantileExchange(CME)onMay16,19722millioncontractstradedin1978230millioncontractstradedin2018CMEGroupformedin2007,throughamergerbetweentheCMEandChicagoBoardofTrade(CBOT)In2008,CMEGroupacquiredtheNewYorkMercantileExchange(NYMEX)7-6Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.CurrencyFuturesMarkets(Continued)MostCMEcurrencyfuturestradeinaMarch,June,September,andDecemberexpirationcycleoutsixquartersintothefuture,withthedeliverydatebeingthethirdWednesdayoftheexpirationmonthLastdayoftradingformostcontractsisthesecondbusinessdaypriortothedeliverydateTradingtakesplaceSundaythroughFridayontheGLOBEXtradingsystemfrom5:00PMto4:00PMChicagotimethenextdayCurrencyfuturestradingtakesplaceonotherexchanges,inadditiontotheCME7-7Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.BasicCurrencyFuturesRelationshipsInformationprovidedonquotesforCMEfuturescontractsincludesthefollowing:Openingprice,highandlowquotesforthetradingday,settlementprice,andopeninterestOpeninterestisthetotalnumberofshortorlongcontractsoutstandingfortheparticulardeliverymonthFuturesarepricesverysimilarlytoforwardcontractsRecallfromchapter6,theIRPmodelstatestheforwardpricefordeliveryattimeTis:7-8Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.OptionContracts:SomePreliminariesAnoptionisacontractgivingtheownertheright,butnowtheobligation,tobuyorsellagivenquantityofanassetataspecifiedpriceatsometimeinfutureOptiontobuyisacall,andoptiontosellisaputBuyingorsellingtheunderlyingassetviatheoptionisknowas“exercising”theoptionStatedpricepaidorreceivedisknownastheexerciseorstrikingpriceBuyerofanoptionisoftenreferredtoasthelong,andthesellerofanoptionisreferredtoasthewriter(ortheshort)Europeanoptioncanbeexercisedonlyatmaturityorexpirationdateofcontract,butAmericanoptioncanbeexercisedanytimeduringcontract7-9Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.CurrencyOptionMarketsPriorto1982,allcurrencyoptioncontractswereOTCoptionswrittenbyinternationalbanks,investmentbanks,andbrokeragehousesOTCoptionsaretailor-madeandgenerallyforlargeamounts(i.e.,atleast$1mofcurrencyservingasunderlyingassets)OTCoptionsaretypicallyEuropeanstyle,andtheyareoftenwrittenforU.S.dollars,withtheeuro,Britishpound,Japaneseyen,Canadiandollar,andSwissfrancservingastheunderlyingcurrencyInDecember1982,PhiladelphiaStockExchange(PHLX)begantradingoptionsonforeigncurrencyIn2008,PHLXwasacquiredbyNASDAQOMXGroup7-10Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.CurrencyFuturesOptionsCMEGrouptradesEuropeanstyleoptionsonseveralofthecurrencyfuturescontractsitoffersWiththese,theunderlyingassetisafuturescontractontheforeigncurrencyinsteadofthephysicalcurrencyOnefuturescontractunderliesoneoptionscontractMostCMEfuturesoptionstradewithexpirationsintheMarch,June,September,DecemberexpirationcycleoftheunderlyingfuturescontractandthreeserialnoncyclemonthsOptionsexpireonthesecondbusinessdaypriortothethirdWednesdayoftheoptionscontractmonthTradingtakesplaceSundaythroughFridayontheGLOBEXsystemfrom5:00PMto4:00PMChicagotimethenextday7-11Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.BasicOption-PricingRelationshipsatExpirationAtexpiration,aEuropeanoptionandanAmericanoption(whichhasnotbeenpreviouslyexercised),bothwiththesameexerciseprice,willhavethesameterminalvalueForcalloptionsthetimeTexpirationvalueperunitofforeigncurrencyisstatedasthefollowing:7-12Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.BasicOption-PricingRelationshipsatExpiration(Continued)Call(put)optionwithST

>E

(E>ST)expiresin-the-moneyItwillbeexercisedbecausethebuyerwillmakemoneyIfST=E,theoptionexpiresat-the-moneyItwillnotbeexercisedbecausenomoneywillbemadebydoingsoIfST

<E

(E<ST),thecall(put)optionexpiresout-of-the-moneyItwillnotbeexercisedbecausethebuyerwouldlosemoneybydoingsoandisundernoobligationtoexercisetheoption7-13Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.AmericanOption-PricingRelationshipsAmericanoptionswillsatisfythefollowingbasicpricingrelationshipsattimetpriortoexpiration:TheaboveequationsstatethattheAmericancallandputpremiumsattimetwillbeatleastaslargeastheimmediateexercisevalue,ortheintrinsicvalue,ofthecallorputoptionLonger-termAmericanoptionwillhaveamarketpriceatleastaslargeastheshort-termoption7-14Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.AmericanOption-PricingRelationships(Continued)Call(put)optionwithST

>E

(E>ST)istradingin-the-moneyIfST?E,theoptionistradingin-the-moneyIfST

<E

(E<ST),thecall(put)optionistradingout-of-the-moneyDifferencebetweentheoptionpremiumandtheoption’sintrinsicvalueisnonnegativeandissometimesreferredtoastheoption’stimevalue7-15Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.MarketValue,TimeValue,andIntrinsicValueofanAmericanCallOption7-16Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.EuropeanOption-PricingRelationshipsPricingboundariesforEuropeanputandcallpremiumsaremorecomplexConsidertwoportfolios:PortfolioAinvolvespurchasingaEuropeancalloptionandlending(orinvesting)anamountequaltothepresentvalueoftheexerciseprice,E,attheU.S.interestrate,i$,whichweassumecorrespondstothelengthoftheinvestmentperiodCostofthisinvestmentisasfollows:Ce

+E/(1+i$)IfST≤E,callownerwillletcalloptionexpireworthlessIfST>E,callownerwillexercisethecall,andexercisevaluewillbeST–E>0PortfolioBconsistsoflendingthepresentvalueofoneunitofforeigncurrency,f,attheforeigninterestrate,if,whichweassumecorrespondstothelengthoftheinvestmentperiodCostofthisinvestmentisSt

/(1+if)7-17Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.EquationforaEuropeanCallOptionLowerBoundary7-18Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.EuropeanOption-PricingRelationships(Continued)Inarationalmarketplace,portfolioAwillbepricedtosellforatleastasmuchasportfolioB,implyingthefollowing:Similarly,itcanbeshownthelowerboundarypricingrelationshipforaEuropeanputis:7-19Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.EuropeanOption-PricingRelationships(Concluded)Basedonthetwoequationsfromtheprecedingslide,itcanbedeterminedthat,whenallelseremainsthesame,thecallpremium,Ce(putpremium,Pe)willincrease:Thelarger(smaller)istheexchangerate,StThesmaller(larger)istheexerciseprice,EThesmaller(larger)istheforeigninterestrate,ifThelarger(smaller)isthedollarinterestrate,i$Thelarger(smaller)i$isrelativetoif7-20Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.EuropeanCallandPutPricesonSpotForeignExchangeEquations7.6and7.7(seeslide19)mayberestatedasthefollowing:7-21Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.EuropeanOption-PricingValuation:Example7.57-22Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.BinomialOption-PricingModelBinomialoption-pricingmodelprovidesanexactpricingformulaforaEuropeancallorputInthiscase,binomialmodelassumesthatattheendoftheoptionperiod,theunderlyingforeignexchangehaseitherappreciatedonestepupwardordepreciatedonestepdownwardfromitsinitialvalueObjectiveistovaluethePHLX112SepEUREuropeancallOptionisquotedatapremiumof3.78centsCurrentspotpriceoftheEURinAmericantermsisS0=113.14centsEstimateoftheoption’svolatilityisσ=6.18percentLastdayoftradinginthecalloptionisin179dayson9/20/19Attheendoftheoptionperiod,theEURwillhaveappreciatedtoSuT=S0

?

uordepreciatedtoSdT=S0

?

d7-23Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.PHLXWorldCurrencyOptionsQuotations7-24Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.BinomialOption-PricingModel(Continued)Binomialoption-pricingmodelreliesontherisk-neutralprobabilitiesoftheunderlyingassetincreasinganddecreasinginvalueRisk-neutralprobabilityoftheEURappreciatingis:q=(FT?S0?d)/S0(u?d)UseSeptemberEURfuturespriceon3/25/19asestimateofFT($/EUR)=$1.1487Therefore,q=(114.87–108.35)/(118.14–108.35)=0.666Binomialcalloptionpremiumisdeterminedby:

C0=[qCuT+(1?q)CdT]/(1+i$)