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1、CHAPTERTHIRTY-SEVENVALUATIONOFBONDSWITHEMBEDDEDOPTIONSFRANKJ.FABOZZI,PH.D.,CFA,CPAFrederickFrankAdjunctProfessorofFinanceSchoolofManagementYaleUniversityANDREWKALOTAY,PH.D.PresidentAndrewKalotayAssociatesMICHAELDORIGAN,PH.D.ConsultingAssociateAndrewKalotayAssociatesThecomplicationinbuildingam
2、odeltovaluebondswithembeddedoptionsandoption-typederivativesisthatcashflowswilldependoninterestratesinthefuture.Academiciansandpractitionershaveattemptedtocapturethisinterest-rateuncertaintythroughvariousmodels,oftendesignedasone-ortwo-factormodels.Thesemodelsattempttocapturethestochasticbehav
3、iorofrates.Inpractice,theseelegantmathematicalmodelsmustbeconvertedtonumericapplications.Herewefocusononesuchmodel—asingle-factormodelthatassumesastationaryvarianceor,asitismoreoftencalled,volatility.Wedemonstratehowtomovefromtheyieldcurvetoavaluationlattice.Effectively,thelatticeisarepre-sen
4、tationofthemodel,capturingthedistributionofratesovertime.Inourillustra-tionwewillreducethelatticetoabinomialtree,themostsimplelatticeform.Thelatticeholdsalltheinformationrequiredtoperformthevaluationofcertainoption-likeinterest-rateproducts.First,thelatticeisusedtogeneratethecashflowsacrossthe
5、lifeofthesecurity.Next,theinterestratesonthelatticeareusedtocomputethepresentvalueofthosecashflows.Thereareseveralinterest-ratemodelsthathavebeenusedinpracticetoconstructaninterest-ratelattice.Thesearedescribedinotherchapters.Ineachcase,interestratescanrealizeoneofseveralpossiblerateswhenwemov
6、efromoneperiodtothenext.Alatticemodelwhereitisassumedthatonlytworatesarepossibleinthenextperiodiscalledabinomialmodel.Alatticemodelwhereitisassumedthatinterestratescantakeonthreepossibleratesinthenextperiodis851Copyright©2005,2001,1997,1995,1991,1987,1983byTheMcGraw-HillCompanies,Inc.Clickher
7、efortermsofuse.852PART5ValuationandAnalysiscalledatrinomialmodel.Thereareevenmorecomplexmodelsthatassumemorethanthreepossibleratesinthenextperiodcanberealized.Regardlessoftheunderlyingassumptions,eachmodelsharesacommonrestriction.Theinterest-
