chapter4-2-金融工程专业无文字缩减新

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1、1Chapter4FuturesandForwardsPricesII2Threekindsofunderlyinginvestmentassets:⑴、Investmentassetsprovidingnoincome⑵、Investmentassetsprovidingaknowncashincome⑶、InvestmentassetsprovidingaknowndividendyieldDeveloppricingmodelsforforwardswhentheunderlyingassethascashflows

2、associatedwithitduringtheperiodoftheforwardcontract.forwardpriceforaninvestmentasset32.2forwardpriceforaninvestmentassetprovidingaKnownCashIncomeIntuition1Toseethis,considerasecuritythathadaperfectlypredicablesetofcashflowsthatwilloccurbetween0andT.Denotethepresentv

3、alueofthosecashflowsasI(discountingattheriskfreerate).Fromtheshortparty’sperspective:buyoneunitoftheassetandenterintoashortforwardcontracttosellitforF0attimeT.ThiscostS0andiscertaintoleadtoacashinflowofF0attimeTandincomewithapresentvalueofI.4AformalproveAssumption:T

4、heunderlyingassetwillprovideincomewithapresentvalueofIduringthelifeofaforwardcontract.Considerthefollowingportfolios(attime0):PortfolioA:alongforwardcontractandacashamountofonhand.PortfolioB:oneunitofunderlyingassetandacashamountofIborrowedatrisk-freeinterestrate.Cl

5、earlyAandBonceagainhavethesamepayoffsattimeT,andsoonceagain,settingthemequivalent:ProvideincomewithapresentvalueofI5ContinuedThisistheforwardpriceforaninvestmentassetprovidingaknowncashincome(presentvalueI).6ReexamineTheFormulaWecouldattributethisformulatothenotiono

6、pportunitycostthattheshortpartyfaced:toinducetheshortpartytoenterintothecontractthelongpartymustpaytheminterestatleastintheamountthattheshortcouldgetiftheysimplysoldtheassetnowandinvesteditattherisk-freerate.Recallthatwedemonstratedthataforwardcontractonasecuritytha

7、tpaysnodividendswillhave,attime0,adeliverypriceof:7ReexamineTheFormulaRecall,however,thatduringtheperiodoftheforwardcontract,iftheshortpartyphysicallyholdstheunderlyingassetprovidingaknowncashincome,thentheywillgarneranybenefitsthataccruetotheassetduringthatperiod.F

8、orexample,iftheforwardcontractwerewrittenonastock,andthestockpaidadividend,theniftheshortpartyphysicallyheldthestockontheex-dividenddate,t