paul wilmott on quantitative finance convertible bonds

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1、CHAPTER33convertiblebondsInthisChapter...•thebasicConvertibleBond(CB)•thepurposeofconvertiblebonds•marketconventionsforthepricingandanalysisofCBs•howtopriceCBsinaone-factorsetting•howtopriceCBsinatwo-factorsetting•featuresthatcanmakeCBspath-dependent33.1INTRODUCTIONT

2、heconversionfeatureofconvertiblebondsmakesthesecontractssimilarmathematicallytoAmericanoptions.Theyarealsoparticularlyinterestingbecauseoftheirdependenceonastockpriceandoninterestrates.Ibeginthischapterwithsomedefinitionsusedbythemarketintheanalysisofconvertiblebonds.

3、Ithenexplainthecontracttermsofthesebondsinaone-factor,stochasticassetpricesetting.Finally,Ishowhowtopriceconvertiblesinatwo-factorworldofstochasticassetandstochasticinterestrate.33.2CONVERTIBLEBONDBASICSTheconvertiblebondorCBonastockpaysspecifiedcouponswithreturnofthe

4、principalatmaturity,unlessatsomeprevioustimetheownerhasconvertedthebondintotheunderlyingasset.Aconvertiblebondthushasthecharacteristicsofanordinarybondbutwiththeextrafeaturethatthebondmay,atatimeoftheholder’schoosing,beexchangedforaspecifiedasset.Thisexchangeiscalledc

5、onversion.ThevalueofaCBisclearlyboundedbelowbyboth•itsconversionvalue,whichistheamountreceivedifthebondisconvertedimmediately(regardlessofwhetherthisisoptimal)conversionvalue=marketpriceofstock×conversionratio.554PartThreefixed-incomemodelingandderivatives•itsvalueasa

6、corporatebond,withafinalprincipalandcouponsduringitslife.Thisiscalleditsstraightvalue.ThelatterpointshowshowtherearecreditriskissuesinthepricingofCBs.Thesecreditriskissuesareveryimportantbutwewillnotdiscusstheminanydetailhere.Weassumethatthereisnoriskofdefault.Creditr

7、iskisdiscussedindepthinChapter40.33.2.1WhatareCBsfor?Companiesissuebondsforthepurposeofraisingcapital.Corporatebondscomeinmany,manyvarieties.Atoneendtherearethesimplevanillabonds,withfixedcouponandrepaymentoftheprincipalatmaturity.Mostcorporatebondshaveacallprovisions

8、othattheissuingcompanycancallthembackpriortomaturity.Theywoulddothisifinterestratesweretofallsufficientlybelowthethenprevailingmarke