chapter4-1无文字金融工程专业

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1、1Chapter4FuturesandForwardsPricesΙ2Ourobjectiveistolinkthepriceofthefuturesorforwardcontracttothepriceoftheunderlyinginstrumentandtoidentifyfactorsthatinfluencetherelationshipbetweentheseprices.ObjectiveofthischapterForwardandfuturespricesSpotpriceoftheunderlyingassetrelationship?Forwardpric

2、esrelationship?31、PRELIMINARIES⑴formanyofthecontractsthataretradedinthemarket,itcanbearguedthattheforwardpriceandfuturespriceofanassetareveryclosetoeachotherwhenthematuritiesofthetwocontractsarethesame.41、PRELIMINARIES⑵notationWewillusealotofnotation,solet’sbeveryclearaboutwhateachsymbolmeans:

3、T=maturitydateoftheforwardcontractt=currenttimeSt=priceofunderlyingattimetST=PriceofunderlyingattimeTK=deliverypriceintheforwardcontractFt=forwardpriceattimetf=valueofalongforwardcontractattimet.r=riskfreerate51、PRELIMINARIES⑶.ContinuousCompoundingCompoundinterestispaidontheoriginalprincipalan

4、dontheaccumulatedpastinterest.Notation:T:Investmentperiod(years)PV:PresentValueofinitialinvestmentFV:FutureValueofinitialinvestmentR:Nominalinterestrateperannumm:Compoundingfrequency6ContinuedWhentheinterestiscompoundedonceayearforTyears:Whatifinterestispaidmorefrequently?Hereareafewexampleso

5、ftheformula:m=1m=4m=127continuedConsideranamountPVinvestedforTyearsataninterestrateofRperannum.Compoundingfrequency(m)m=1m>1m→Futurevalueafternyears(FV)Thelimitasmtendstoinfinityisknownascontinuouscompounding8示例例：假设存款金额为100，名义年利率为10%，存款期限为1年，在年度计息的条件下，明年的期末存款余额为：100×1.1=110半年计息一次：100×1.05×1.05

6、=110.25每季度计息一次：100×1.0254＝110.38连续复利：100×e0.10=110.529实际利率与计息次数10continuedThelimitasmtendstoinfinityisknownascontinuouscompoundingThestandardfutureandpresentvalueformulasare:PV→FV：PV*eRT＝FVFV→PV：FV*e-RT＝PVForexample,ifyourdiscountrateis8%,andyouaregoingtoreceive$200in2years,thepresentvalueofth

7、atcashflowis:11continuedYoushouldbeawareofhowtoconvertbetweeninterestratesofdifferentcompoundingfrequency.Forexample,ifryistheannuallycompoundedrateofreturnwhatistheequivalentquarterlycompoundedrateofreturn?Youcansetthisupeasilyenoughby