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1、Chapter28 MartingalesandMeasuresOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20141DerivativesDependentonaSingleUnderlyingVariableOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20142FormingaRisklessPortfolioOptions,Futures,an
2、dOtherDerivatives,9thEdition,Copyright©JohnC.Hull20143MarketPriceofRisk(Page657)Thisshowsthat(m–r)/sisthesameforallderivativesdependentonthesameunderlyingvariable,qWereferto(m–r)/sasthemarketpriceofriskforqanddenoteitbylOptions,Futures,andOtherDerivatives,9thEdition
3、,Copyright©JohnC.Hull20144ExtensionoftheAnalysis toSeveralUnderlyingVariables(Equations28.12and28.13,page659)Options,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20145Martingales(Page660-661)AmartingaleisastochasticprocesswithzerodriftAvariablefollowin
4、gamartingalehasthepropertythatitsexpectedfuturevalueequalsitsvaluetodayOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20146AlternativeWorldsOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20147TheEquivalentMartingaleMeasureResu
5、lt(Page660-661)Options,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20148ForwardRiskNeutralityWewillrefertoaworldwherethemarketpriceofriskisthevolatilityofgasaworldthatisforwardriskneutralwithrespecttog.IfEgdenotesexpectationsinaworldthatisFRNwrtgOptio
6、ns,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20149AlternativeChoicesfortheNumeraireSecuritygMoneyMarketAccountZero-couponbondpriceAnnuityfactorOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull201410MoneyMarketAccount astheNumeraire
7、Themoneymarketaccountisanaccountthatstartsat$1andisalwaysinvestedattheshort-termrisk-freeinterestrateTheprocessforthevalueoftheaccountisdg=rgdtThishaszerovolatility.Usingthemoneymarketaccountasthenumeraireleadstothetraditionalrisk-neutralworldwherel=0Options,Futures
8、,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull201411MoneyMarketAccount continuedOptions,Futures,andOtherDerivatives,9thEdition,Copyr
