货币时间价值与利率期限结构清华大学绝版金融工程

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1、CHAPTERTWO:TimeValueofMoneyandTermStructureofInterest1Yes!istheexpectedrateofreturn,i.e.,themeanofthediscountratesfordifferenttermsLetNo!isthediscountratethatcannotbeusedforsolongperiod?DiscountedCashFlowFormula2TermStructureofInterestRatesOurobjectiveistovaluerisklesscashflows.Giventh

2、erichsetoffixed-incomesecuritiestradedinthemarket,theirpricesprovidetheinformationneededtovaluerisklesscashflowsathand.3FormsofInterestRatesInthismarket,thisinformationonthetimevalueofmoneyisgiveninseveraldifferentforms:SpotinterestratesPriceofdiscountbonds(e.g.,zero-couponbondsandSTRI

3、PS)PricesofcouponbondsYield-to-maturity(anaverageofspotinterestrates)ForwardinterestratesTheforminwhichthisinformationisexpresseddependsontheparticularmarket.4DeterminationofInterestRateCapitalproductionability——themorethecapital’sexpectedreturn,thehighertheinterestratesandviceversa.Un

4、certaintyofcapitalproductionability——themoretheuncertainty,thehighertheriskpremiumrequiredandthehighertheinterestratesandviceversa.Timepreferenceofconsumption——thestrongerpreferencetocurrentconsumption,thehighertheriskpremiumrequiredandthehighertheinterestratesandviceversa.Riskaversion

5、——themoretheriskaversion,thehighertheriskpremiumrequiredandthelowertherisk-freeinterestrates.Fourbasicfactors5TheoryofRealInterestRatesRealinterestratesaredeterminedbysupplyanddemandoffundsintheeconomy.3factorsindeterminingrealinterestrates:AggregateendowmentsAggregateinvestmentopportu

6、nitiesAggregatepreferencesfordifferentconsumptionpath6Considerarepresentativeinvestor:Hasendowmentof(e0,e1)Facesabondmarketwithinterestrater.7Hemaximizeshisutilityoverhisconsumptionnowandlater:Wherebisthebondholding,u’>0andu”<08TheoptimalityconditionisRelativeriskaversioncoefficientThu

7、s,therealinterestrateisgivenby9NonlineartechnologyTime0Time1-(1+RC)Investmentopportunitysetbb(1+r)10LineartechnologyTime0Time1b(1+r)b-(1+RC)11Moregenerally,considerconsumptiongrowatrandomrate.Investorsmaximizetheirexpectedutilityovermanyperiods.Whereishisholdingsofdiscountbonds,isfut