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1、PricingInterest-Rate-DerivativeSecuritiesJohnHullAlanWhiteUniversityofTorontoThisarticleshowsthattheone-state-variableinterest-ratemodelsofVasicek(1977)andCox,Ingersoll,andRoss(1985b)canbeextendedsothattheyareconsistentwithboththecurrenttermstructureof
2、interestratesandeitherthecurrentvolatilitiesofallspotinterestratesorthecurrentvolatilitiesofallforwardinterestrates.TheextendedVasicekmodelisshowntobeverytracta-bleanalytically.ThearticlecomparesoptionpricesobtainedusingtheextendedVasicekmodelwiththose
3、obtainedusinganumberofothermodels.Inrecentyears,interest-rate-contingentclaimssuchascaps,swaptions,bondoptions,captions,andmort-gage-backedsecuritieshavebecomeincreasinglypopular.Thevaluationoftheseinstrumentsisnowamajorconcernofbothpractitionersandaca
4、demics.Practitionershavetendedtousedifferentmodelsforvaluingdifferentinterest-rate-derivativesecuri-ties.Forexample,whenvaluingcaps,theyfrequentlyassumethattheforwardinterestrateislognormalanduseBlacks(1976)modelforvaluingoptionsoncom-modityfutures,The
5、volatilityoftheforwardrateisassumedtobeadecreasingfunctionofthetimetomaturityoftheforwardcontract.WhenvaluingEuro-ThisresearchwasfundedbytheSocialSciencesandHumanitiesResearchCouncilofCanada.WewouldliketothankMichaelBrennan,EmanuelDerman,FarshidJamshid
6、ian,CalJohnson,MarkKoenigsberg,JohnRumsey,ArmandTatevossian,YisongTian,StuartTurnbull,KenVetzel,andpartici-pantsoffinanceworkshopsatDukeUniversity,QueensUniversity,andtheUniversityofTorontoforhelpfulcommentsonanearlierdraftofthispaper.Addressreprintreq
7、ueststoJohnHull,FacultyofManagement,UniversityofToronto,246BloorStreetWest,Toronto,Ontario,CanadaM5S1V4.TheReviewofFinancialStudies1990Volume3,number4,pp.573-392©1990TheReviewofFinancialStudies0893-9454/90/$1.50TheReviewofFinancialStudies/v3n41990peanb
8、ondoptionsandswaptions,practitionersoftenalsouseBlacks(1976)model.However,inthiscase,forwardbondpricesratherthanforwardinterestratesareassumedtobelognormal.Usingdifferentmodelsindifferentsituationshasanumberofdis-advantages.First,therei
