金融工程课堂展示.ppt

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1、OPTIONS、FUTURES&OTHERDERIVATIVESSTUDENTPRESENTATIONTUTOR：PROFYE指导老师：叶永刚教授STUDENTNAME：HEHAO学生姓名：贺昊NO.：2003210507731ExtensionoftheTheoreticalFrameworkforPricingDerivatives;MartingalesandMeasuresChapter192DerivativesDependentonaSingleUnderlyingVariable3FormingaRisklessPortfolio

2、4MarketPriceofRisk(Page500)Thisshowsthat(m–r)/sisthesameforallderivativesdependentonthesameunderlyingvariable,qWereferto(m–r)/sasthemarketpriceofriskforqanddenoteitbyl5DifferentialEquationforƒ(Equation19.10,page501)UsingIto’slemmatoobtainexpressionsformandsintermsofmands.Theequa

3、tionm-ls=rbecomes6Risk-NeutralValuationThedifferentialequationshowsthatqislikeastockpricepayingadividendyieldofr–m+lsThisanalogyshowsthatwecanvalueƒinarisk-neutralworldprovidingthedriftrateofqisreducedfrommtom–ls7ExtensionoftheAnalysistoSeveralUnderlyingVariables(Equations19.12

4、and19.13,page503)8DerivativesDependentonCommodityPrices(Page506)Foracommoditythefuturespricegivestheexpectedvalueinthetraditionalrisk-neutralworld9Martingales(Page507)AmartingaleisastochasticprocesswithzerodrfitAmartingalehasthepropertythatitsexpectedfuturevalueequalsitsvaluetod

5、ay10AlternativeWorlds11AKeyResult(Page509)12ForwardRiskNeutralityWerefertoaworldwherethemarketpriceofriskisthevolatilityofgasaworldthatisforwardriskneutralwithrespecttog.IfEgdenotesaworldthatisFRNwrtg13AleternativeChoicesfortheNumeraireSecuritygMoneyMarketAccountZero-couponbondp

6、riceAnnuityfactor14MoneyMarketAccountastheNumeraireThemoneymarketaccountisanaccountthatstartsat$1andisalwaysinvestedattheshort-termrisk-freeinterestrateTheprocessforthevalueoftheaccountisdg=rgdtThishaszerovolatility.Usingthemoneymarketaccountasthenumeraireleadstothetraditionalr

7、isk-neutralworld15MoneyMarketAccountcontinued16Zero-CouponBondMaturingattimeTasNumeraire17ForwardPricesInaworldthatisFRNwrtP(0,T),theexpectedvalueofasecurityattimeTisitsforwardprice18InterestRatesInaworldthatisFRNwrtP(0,T2)theexpectedvalueofaninterestratelastingbetweentimesT1an

8、dT2istheforwardinterestrate19AnnuityFactorasthe