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1、TheValuationofAmerican1OptionsonBonds223T.S.Ho,RichardC.Stapleton,andMartiG.SubrahmanyamApril16,1997Keywords:AmericanBondOptions,StochasticInterestRatesJELClassi cation:G111EarlierversionsofthispaperhavebeenpresentedattheEuropeanFinanceAssociationmeetinginRotter
2、dam,attheFinancialOptionsResearchCentre,WarwickUniversity,andattheHongKongUniversityofScienceandTechnology.WethankAnuragGuptaforableresearchassistance.Wewouldalsoliketothankananonymousrefereefordetailedcommentsonanearlierdraftofthepaper.2DepartmentofAccountingan
3、dFinance,TheManagementSchool,LancasterUniversity,LancasterLA14YX,UK.Tel:+441524593637,Fax:+441524847321,e-mail:dj@staplet.demon.co.uk3LeonardN.SternSchoolofBusiness,NewYorkUniversity,ManagementEd-ucationCenter,44West4thStreet,Suite9{190,NewYork,NY10012{1126,USA.
4、Tel:+12129980348,Fax:+12129954233,e-mail:msubrahm@stern.nyu.edu.PleasesendproofstoMartiG.Subrahmanyam.AbstractWevalueAmericanoptionsonbondsusingageneralizationoftheGeske{Johnson(1984)technique.ThemethodrequiresthevaluationofEuropeanoptions,andoptionswithmultiple
5、exercisedates.Itisshownthatarisk-neutralvaluationrelationshipalongthelinesofBlack{Scholes(1973)modelholdsforoptionsexercisableonmultipledates,evenunderstochasticinterestrates,whenthepriceoftheunderlyingassetislognormallydistributed.Theproposedcomputationalproced
6、ureusesthemaximizedvalueoftheseoptions,wherethemaximizationisoverallpossibleexercisedates.ThevalueoftheAmericanoptionisthencomputedbyRichardsonextrapolation.Thevolatilityoftheunderlyingdefault-freebondismodelledusingatwo-factormodel,withashort-termandalong-termi
7、nterestratefactor.WereporttheresultsofsimulationsofAmericanoptionvaluesusingourmethodandshowhowtheyvarywiththekeyparameterinputs,suchasthematurityofthebond,itsvolatility,andtheoptionstrikeprice.ValuationofAmericanBondOptions11IntroductionThevaluationofAmerican-s
8、tylebondoptionsinvolvestwoimportantaspectsthatneedtobemodelledcarefully.First,stochasticinterestratesin
uencethevolatilityofthepriceofthebond,theunderlyingasset,inaco
