第八章外匯期權(quán)

重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅1Chapter6ForeignCurrencyOptions重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅2referenceFundamentalsofMultinationalFinance(3rdE)ByMoffett,Stonehill,andEitemanPublisher:AddisonWesleyPublicationDate:2008-02-18FundamentalsofFuturesandOptionsMarkets(4thE)ByJohnC.HullPublisher:PrenticeHallPublicationDate:2002重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅3LearningObjectivesUnderstandwhatforeigncurrencyoptionisExaminehowforeigncurrencyoptionsarequotedAnalyzeforeigncurrencyoptionspeculationObtainbasicknowledgeonforeigncurrencyoptionpricing重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅46.1Options:SomeDefinitionsAMiniCase:DongguanCity重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅56.1.1DefinitionAforeigncurrencyoptionisanagreementbetweentwoparties(the‘buyer’oftheoptionand‘theseller’oftheoption)thatgivesthebuyeroftheoptiontheright,butnottheobligation,toexchangeaspecifiedamount(‘thefacevalue’)ofonecurrencyforanothercurrencyatanominatedforeignexchangerateonanominatedfuturedate.重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅6ThreeElementPricesSpotRate,StExercise/StrikePriceEPremiumc重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅76.1.2TypesofOptionsBasicTypesoptionsCalloptionPutoptionBuyerofcalloptionIfexerciseoptionHastherightbutnotobligationtopurchaseunderlyingassetwithanagreedpriceWriterofcalloptionIfoptionexercisedHasobligationtoSellunderlyingassetWithanagreedpriceBuyerofputoptionIfexerciseoptionHastherightbutnotobligationtosellunderlyingassetwithanagreedpriceWriterofputoptionIfoptionexercisedHasobligationtobuytheunderlyingassetWithanagreedprice重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅8CategorizedbytheCharacteristicsVanillaOption:AmericanoptionandEuropeanoptionExoticOptioncurrencyswaption,Bermudanoption,binaryoption,Asianoption,lookbackoption,ratchetoption,barrieroption,etc.重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅9CategorizedbytheUnderlyingAssetCurrencyOptionCurrencyFuturesOptionFutures-StyleOptionCompoundOption重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅10CategorizedbytheTradingVenueExchange-TradedOptionOver-the-Counter(OTC)重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅116.1.3ForeignCurrencyOptionsMarketsOver-the-CounterMarketexoticcurrencyoptionsmarketvolumedominantsthewholeoptionmarketcounterpartyriskOrganizedExchangesNASDAQOMXPHLX(PHLX)

CME重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅12ComparisonPricingLocationContractArticlesSettlementDeliveryRisksCounterpartiesTradingHours&RegulationsLiquidity重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅136.1.4CurrencyOptionQuotationConventions

重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅14EuroOptionsCallsPutVOLLASTVOLLASTEuro88.1562,500Euro-centsperunit88Apr--100.4390Jun222.3412.3594Mar--33.65114Mar--223.55重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅15SwissFrancOptionsCallsPutVOLLASTVOLLASTSFranc57.8362,500SwissFrancs-centsperunit58Apr61.38--60Sep21.90--重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅16Exercise1WhatisthequotationforMarchputoptiononJapaneseyen?CallsPutVOLLASTVOLLASTJapaneseyen93.156,250,000J.yen-100thsofacentperunit8150Mar--50.308250Apr21.1021.4483Apr--51.51重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅17Sum:PhiladelphiaExchangeOptions

asof15thDec.2000Spotrate,88.15￠/€Sizeofcontract:

€62,500Exerciseprice

90￠/€Theindicatedcontractpriceis:

€62,500$0.0125/€=$781.25Onecalloptiongivestheholdertherighttopurchase

€62,500for$56,250(=€62,500$0.90/€)Optionpriceforpurchaseof€1at90￠is1.25￠MaturitymonthOnecalloptiongivestheholder

therighttopurchase

€62,500for$56,250.Thisoptioncosts$781.25.重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅18重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅196.2SpeculatinginOptionMarkets6.2.1BuyerofaCallProfit&Loss0-cEST45oBreak-evenPrice=E+cExercisecalloptionUnlimitedprofitLimitedloss重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅206.2.3WriterofaCallProfit&Loss0-cEST45oE+cCalloptionexercisedUnlimitedlossLimitedprofit=cc重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅216.2.4BuyerofaPutProfit&Loss0-cEST45oBreak-evenPrice=E-cExerciseputoptionProfituptoE-cLimitedloss重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅226.2.5WriterofaPutProfit&Loss0EST45oE-cPutoptionexercisedLossuptoE-cLimitedgain=cc重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅23Exercise2Profit/LossCallputbuyerwritersumbuyerwritersumST<EST=EST>E重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅246.3BasicTheoriesonOptionPricing6.3.1GeneralTheories:IntrinsicValueandTimeValue/ExtrinsicValueIntrinsicvalueisthefinancialgainiftheoptionisexercisedimmediately.Underno-arbitragerule,intrinsicvalueislessthanpremium.ITMATMOTMAtExpiration重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅252)TimeValue/ExtrinsicValueThedifferencebetweentheoptionpremiumandtheoption’sintrinsicvalueisnonnegative,andreferredtoastheoption’sTimeValue.Thetimevalueispositivelycorrelatedwiththetimetomaturity.Therationalefortimevalue重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅263)TheProfit/LossProfile重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅274)OptionGreeksOptionDelta,δOptionGamma,γOptionVega,υO(shè)ptionTheta,θ重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅28δ=cs重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅29γ=css重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅30υ=cσ重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅31θ=ct重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅326.3.2BasicPrinciplesforOptionPricingOptionValuesatexpirationCeT=Max[ST-E,0]andPeT=Max[E-ST,0]Cat≥St-E,Pat≥E-St,where0≤t≤T2)OptionPricesareNonnegativeCe≥0andPe≥0;Ca≥0andPa≥03)UpperBoundariesforEuropeanCurrencyOptionsCet≤StandPet≤Ee-i*τ重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅334)LowerBoundariesforEuropeanCurrencyOptionsCet≥e-i*τST-e-iτEPet≥e-iτE-e-i*τST

Port-foliosPresentValueFutureValueST≤EST>EICet+e-iτEESTIIe-i*τSTSTST重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅345)Put-callParityforEuropeanCurrencyOptionsPortfolioIPresentValueFutureValueST<EST≥

ELongputPetE-ST0Shortcall-Cet0E-STSumPet-CetE-STE-ST重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅355)Put-callParityforEuropeanCurrencyOptionsPortfolioIIPresentValueFutureValueST<EST≥

ELongdomesticbonde-iτEEEShortforeignbond-e-i*τST-ST-STSume-iτE-e-i*τSTE-STE-ST重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅365)Put-callParityforEuropeanCurrencyOptionsPet-Cet=e-iτE-e-i*τST重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅376)TimeValueforAmericanCurrencyOptionsCa(T-t0)≥Ca(T-t1)andPa(T-t0)≥Pa(T-t1)T≥t1>t0,T-t0andT-t1betimestoexpiration重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅387)LowerBoundariesforAmericanCurrencyOptionsCat≥Max[0,St-E,e-i*τST-e-iτE]Pa≥Max[0,E-St,e-iτE-e-i*τST]重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅398)Put-callParityforAmericanCurrencyOptionsCat+E-e-i*τSt≥Pat≥Cat+e-iτE-St重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅406.3TheBlack-ScholesModelforEuropeanCurrencyOptionsAssumptionsandExplanationFrictionlessMarketCondition:notransactioncost.Allmarketparticipantsarepricetakers;Allinterestratesarerisklesscontinuouslycompoundedrates,anddonotchangeoverthetermoftheoptions.Theperformanceofthespotexchangeratefollowstheweakformmarketefficiency.重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅41ItoProcessdSt=μtStdt+σStdztμistheriskpremiumonSt;dtisaninstantintime;σistheoreticalvolatilityofSt;dztisthedifferentialofastochasticvariable.Brownmotiondztfollowstherule重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅42ΔzΔtdzdtΔzΔz2=Δt0dzd2z=dt0ΔtΔtΔz=00dtdtdz=00Ito’sLemmaTaylorseriesexpansionforCet=f(St,t)isdf=fsds+ftdt+?fssds2+fstdsdt+?fttdt2+…→df=(fsμSt+ft+?fssσ2St2)dt+σStfsdztLetG=lnSt,thenGs=1/St,Gt=0,Gss=-1/St2dG=(GsμSt+Gt+?Gssσ2St2)dt+σStGsdztTakeintegralfromttoTlnST=lnSt+(μ-)(T-t)+σε重慶工商大學(xué)財(cái)政金融學(xué)院陶慶梅43DerivetheB-SModelTheTaylorseriesexpansionforEuropeancallpremiumf(St,t)isdf=(fsμSt+ft+?fssσ2St2)dt+σStfsdztThecorrespondingdiscreteformisΔf=(fsμSt+ft+?fssσ2St2)Δt+σStfsΔzImposeΔS=μStΔt+σStΔz.InordertoeliminateΔz,shortaEuropeancalloptionwithoptionvalueoff,theexpirationdateisattime