金融工程专业无文字缩减新.ppt

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1、1Chapter4FuturesandForwardsPricesII2Threekindsofunderlyinginvestmentassets:⑴、Investmentassetsprovidingnoincome⑵、Investmentassetsprovidingaknowncashincome⑶、InvestmentassetsprovidingaknowndividendyieldDeveloppricingmodelsforforwardswhentheunderlyingassethascashflowsassociatedwi

2、thitduringtheperiodoftheforwardcontract.forwardpriceforaninvestmentasset32.2forwardpriceforaninvestmentassetprovidingaKnownCashIncomeIntuition1Toseethis,considerasecuritythathadaperfectlypredicablesetofcashflowsthatwilloccurbetween0andT.DenotethepresentvalueofthosecashflowsasI(

3、discountingattheriskfreerate).Fromtheshortparty’sperspective:buyoneunitoftheassetandenterintoashortforwardcontracttosellitforF0attimeT.ThiscostS0andiscertaintoleadtoacashinflowofF0attimeTandincomewithapresentvalueofI.4AformalproveAssumption:Theunderlyingassetwillprovideincomewi

4、thapresentvalueofIduringthelifeofaforwardcontract.Considerthefollowingportfolios(attime0):PortfolioA:alongforwardcontractandacashamountofonhand.PortfolioB:oneunitofunderlyingassetandacashamountofIborrowedatrisk-freeinterestrate.ClearlyAandBonceagainhavethesamepayoffsattimeT,and

5、soonceagain,settingthemequivalent:ProvideincomewithapresentvalueofI5ContinuedThisistheforwardpriceforaninvestmentassetprovidingaknowncashincome(presentvalueI).6ReexamineTheFormulaWecouldattributethisformulatothenotionopportunitycostthattheshortpartyfaced:toinducetheshortpartyto

6、enterintothecontractthelongpartymustpaytheminterestatleastintheamountthattheshortcouldgetiftheysimplysoldtheassetnowandinvesteditattherisk-freerate.Recallthatwedemonstratedthataforwardcontractonasecuritythatpaysnodividendswillhave,attime0,adeliverypriceof:7ReexamineTheFormulaRe

7、call,however,thatduringtheperiodoftheforwardcontract,iftheshortpartyphysicallyholdstheunderlyingassetprovidingaknowncashincome,thentheywillgarneranybenefitsthataccruetotheassetduringthatperiod.Forexample,iftheforwardcontractwerewrittenonastock,andthestockpaidadividend,thenifthe

8、shortpartyphysicallyheldthestockontheex-dividenddate,t