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1、CHAPTER33convertiblebondsInthisChapter...?thebasicConvertibleBond(CB)?thepurposeofconvertiblebonds?marketconventionsforthepricingandanalysisofCBs?howtopriceCBsinaone-factorsetting?howtopriceCBsinatwo-factorsetting?featuresthatcanmakeCBspath-dependent33.1INTRODUCTIONT
2、heconversionfeatureofconvertiblebondsmakesthesecontractssimilarmathematicallytoAmericanoptions.Theyarealsoparticularlyinterestingbecauseoftheirdependenceonastockpriceandoninterestrates.Ibeginthischapterwithsomede?nitionsusedbythemarketintheanalysisofconvertiblebonds.
3、Ithenexplainthecontracttermsofthesebondsinaone-factor,stochasticassetpricesetting.Finally,Ishowhowtopriceconvertiblesinatwo-factorworldofstochasticassetandstochasticinterestrate.33.2CONVERTIBLEBONDBASICSTheconvertiblebondorCBonastockpaysspeci?edcouponswithreturnofthe
4、principalatmaturity,unlessatsomeprevioustimetheownerhasconvertedthebondintotheunderlyingasset.Aconvertiblebondthushasthecharacteristicsofanordinarybondbutwiththeextrafeaturethatthebondmay,atatimeoftheholder’schoosing,beexchangedforaspeci?edasset.Thisexchangeiscalledc
5、onversion.ThevalueofaCBisclearlyboundedbelowbyboth?itsconversionvalue,whichistheamountreceivedifthebondisconvertedimmediately(regardlessofwhetherthisisoptimal)conversionvalue=marketpriceofstock×conversionratio.554PartThree?xed-incomemodelingandderivatives?itsvalueasa
6、corporatebond,witha?nalprincipalandcouponsduringitslife.Thisiscalleditsstraightvalue.ThelatterpointshowshowtherearecreditriskissuesinthepricingofCBs.Thesecreditriskissuesareveryimportantbutwewillnotdiscusstheminanydetailhere.Weassumethatthereisnoriskofdefault.Creditr
7、iskisdiscussedindepthinChapter40.33.2.1WhatareCBsfor?Companiesissuebondsforthepurposeofraisingcapital.Corporatebondscomeinmany,manyvarieties.Atoneendtherearethesimplevanillabonds,with?xedcouponandrepaymentoftheprincipalatmaturity.Mostcorporatebondshaveacallprovisions
8、othattheissuingcompanycancallthembackpriortomaturity.Theywoulddothisifinterestratesweretofallsuf?cientlybelowthethenprevailingmarke
