value of the firm and the risk of default

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1、CHAPTER39valueofthefirmandtheriskofdefaultInthisChapter...•modelsfordefaultbasedonthe‘valueofthefirm’•modelingthevalueofafirmbasedonmeasurableparametersandvariables39.1INTRODUCTIONSofar,theproductsonwhichwehaveconcentratedhaveallhadcashflowsthatareguaranteed.Wehaveassumedthatthesecashflows,coupons

2、,payoffsandredemptionvalues,arefromacompletelycreditworthysourceorunderwritteninsuchawaythattheincomeiscertain.Optionsboughtthroughanexchangeareusuallyconsideredfreeoftheriskofdefaultbecauseofthewaythatexchangesareunderwritten,andpartlybecauseoftherequirementforamargintobedeposited.Inpractice

3、,manybondshavenosuchguarantee.Perhapstheyareissuedbyacompanyasaformofborrowingforexpansion.Inthiscase,theissuingcompanymaydeclarebankruptcybeforeallofthecashflowshavebeenpaid.Alternatively,theymaybeissuedbyagovernmentwitharecordforirregularpaymentofdebt.Overthecounter(OTC)optionscanhavesignific

4、antcounterpartyrisks.Forthisreasontherehasgrownupoverthepastdecadeaconsiderablebodyofrulesandregulationsgoverningcapitaladequacy,toensurethatbanksarecoveredintheeventofextrememarketmovementsthatmightotherwiseleadtocollapse(seeChapter19onValueatRisk).Inthischapterwediscussthesubjectofmodelingw

5、henthereisriskofdefaultorcreditrisk.Therearetwomainapproachestothemodelingofdefault.Onerevolvesaroundmodelingthevalueoftheissuingfirm(orcountry).Theothermodelsanexogenousriskofdefault.Theformerisappealingbecauseitisclearlyclosertoreality.Thedownsideisthatthesemodelsareusuallymorecomplicatedtos

6、olve,withparametersthataredifficulttomeasure.Idescribethemostpopularsuchmodelandthendescribeasimilarmodel,onewithmoreeasily-measuredparameters.640PartFourcreditrisk39.2THEMERTONMODEL:EQUITYASANOPTIONONACOMPANY’SASSETSTheMertonmodelshowsveryelegantlyhowtheequityofacompanycanbethoughtofasasimple

7、calloptionontheassetsofthecompany.HestartsoffbyassumingthattheassetsofthecompanyAfollowarandomwalkdA=µAdt+σAdX.Clearly,thevalueoftheequityequalsassetslessliabilities:S=A−V.HereSisthevalueoftheequity(justtheshareprice,I’veassumedthatthereisonl