CH04_Interest Rates and Duration(久期)(金融工程-华东师范大学 汤银才)课件.ppt

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1、InterestRatesandDuration(久期)Chapter4TypesofRatesTreasuryrates（国债利率）—regardedasrisk-freeratesLIBORrates(LondonInterbankOfferrate)(伦敦银行同业放款利率)–generallyhigherthanTreasuryzeroratesReporates(回购利率)—slightlyhigherthantheTreasuryratesZeroRatesAzerorate(orspotrate),format

2、urityT,istherateofinterestearnedonaninvestmentthatprovidesapayoffonlyattimeT.Inpractice,itisusuallycalledzero-couponinterestrate(零息票利率).Example(Table4.1,page89)BondPricingTocalculatethecashpriceofabondwediscounteachcashflowattheappropriatezerorateInourexample(page8

3、9),thetheoreticalpriceofatwo-yearbondwithaprincipalof$100providinga6%couponsemiannuallyisBondYieldThebondyieldisthediscountratethatmakesthepresentvalueofthecashflowsonthebondequaltothemarketpriceofthebondSupposethatthemarketpriceofthebondinourexampleequalsitstheore

4、ticalpriceof98.39Thebondyieldisgivenbysolvingtogety=0.0676or6.76%.ParYieldTheparyield(面值收益率)foracertainmaturityisthecouponratethatcausesthebondpricetoequalitsfacevalue(ie.Theprincipal).Thebondisusuallyassumedtoprovidesemiannualcoupons.InourexamplewesolveParYield(co

5、ntinued)Ingeneralifmisthenumberofcouponpaymentsperyear,Pisthepresentvalueof$1receivedatmaturityandAisthepresentvalueofanannuity(年金)of$1oneachcoupondateSampleData(Table4.2,page91))BondTimetoAnnualBondPrincipalMaturityCouponPrice(dollars)(years)(dollars)(dollars)100

6、0.25097.51000.50094.91001.00090.01001.50896.01002.0012101.6TheBootstrapMethod(息票剥离法)--usedtodeterminezeroratesAnamount2.5canbeearnedon97.5during3months.The3-monthrateis4times2.5/97.5or10.256%withquarterlycompoundingThisis10.13%withcontinuouscompoundingSimilarlythe6

7、monthand1yearratesare10.47%and10.54%withcontinuouscompoundingTheBootstrapMethod（continued）Tocalculatethe1.5yearratewesolvetogetR=0.1068or10.68%Similarlythetwo-yearrateis10.81%（seetheequationonpage91）ZeroCurveCalculatedfromtheData(Figure4.1,page92)ZeroRate(%)Maturit

8、y(yrs)10.12710.46910.53610.68110.808ForwardRates(远期利率)Theforwardrateisthefuturezerorateimpliedbytoday’stermstructure(期限结构)ofinterestratesItisdet