Counterparty risk and the pricing of defaultable s

CounterpartyRiskandthePricingofDefaultableSecuritiesRobertA.JarrowandFanYu∗∗JarrowisfromtheJohnsonGraduateSchoolofManagement,CornellUniversityandKamakuraCorporation,andYuisfromtheGraduateSchoolofManagement,UniversityofCaliforniaatIrvine.ApreviousversionofthispaperappearedasChapter1ofYu’sdoctoraldissertationatCornellUniversity.WethankWarrenBailey,RichardGreen(theeditor),HaitaoLi,RobertMasson,GeorgeOldfield,GeorgePennacchi,ananonymousreferee,andseminarparticipantsatBaruchCollege,BostonUniversity,theCollegeofWilliamandMary,CornellUniversity,theFederalReserveBankofNewYork,GeorgetownUniversity,McGillUniversity,RiceUniversity,theUniversityofBritishColumbia,theUniversityofCaliforniaatIrvine,theUniversityofIllinoisatUrbana-Champaign,theUniversityofIowa,theUniversityofWyoming,the2000DerivativesSecuritiesConferenceatBostonUniversity,andthe1999FrankBattenYoungScholarsConferenceattheCollegeofWilliamandMaryforusefulcomments.YuacknowledgesthesupportofaSageGraduateFellowshipfromCornellUniversitywhilepartofthisresearchwascompleted.CounterpartyRiskandthePricingofDefaultableSecuritiesAbstractMotivatedbyrecentfinancialcrisesinEastAsiaandtheU.S.wherethedownfallofasmallnumberoffirmshadaneconomy-wideimpact,thispapergeneralizesexistingreduced-formmodelstoincludedefaultintensitiesdependentonthedefaultofacounterparty.Inthismodel,firmshavecorrelateddefaultsduenotonlytoanexposuretocommonriskfactors,butalsotofirm-specificrisksthataretermed“counterpartyrisks.”Numericalexamplesillustratetheeffectofcounterpartyriskonthepricingofdefaultablebondsandcreditderivativessuchasdefaultswaps.IthasbeenwelldocumentedinMoody’sreportsonhistoricaldefaultratesofcorporatebondissuersthatthenumberofdefaults,thenumberofcreditratingdowngrades,andcreditspreadsareallstronglycorrelatedwiththebusinesscycle.Thishasmotivatedreduced-formmodelssuchasDuffieandSingleton(1999)andLando(1994,1998),whichassumethattheintensityofdefaultisastochasticprocessthatderivesitsrandomnessfromasetofstatevariablessuchastheshort-terminterestrate.Thisapproachhastheconvenientfeaturesthatconditioningonthestatevariables,defaultsbecomeindependentevents,anddefaultcorrelationarisesduetothecommoninfluenceofthesestatevariables.Ontheotherhand,adefaultintensitythatdependslinearlyonasetofsmoothlyvaryingmacroeconomicvariablesisunlikelytoaccountfortheclusteringofdefaultsaroundaneconomicrecession.ThisisevidentfromacasualinspectionoftheexhibitsinthelatestMoody’sreport(seeKeenan(2000)).Withintheusualaffineframework,onecanmodelthestatevariablesasjumpdiffusions(seeDuffie,PanandSingleton(1999)).Butpresentlythereisnoevidencewhetherthemagnitudeofjumpsneededtojustifytheclusteringofdefaultsisconsistentwithwell-defined,observablemacroeconomicvariables.1Thispapercomplementsthecurrentliteratureondefaultriskmodelingbyintroducingtheconceptofcounterpartyrisk.Inourmodel,eachfirmhasaunique(firm-specific)counterpartystructurethatarisesfromitsrelationwithotherfirmsintheeconomy.Counterpartyriskistheriskthatthedefaultofafirm’scounterpartymightaffectitsowndefaultprobability.Thisapproachhastwobenefits.First,totheextentthatthepublicisawareofthecounterpartyrelations,thepricesofmarketedsecuritieswillreflectthemarket’sassessmentoftheimportanceofcounterpartyrisk.Relyingonthenotionofmarketefficiency,ourmodelallowstheextractionofthisinformation,whichispotentiallyimportantforthepricingofdefaultablebondsandcreditderivatives,aswedemonstratebelow.Second,theadditionaldefaultcorrelationintroducedbycounterpartyrelationsmakesitstraightforwardtoaccountfortheobservedclusteringofdefaults.Forinstance,agroupoffirmscanbesohighlyinterdependentthatasingledefaultcantriggeracascadeofdefaults.Becausethelikelihoodofdefaultishigherforallfirmsduringarecession,thiscascadingeffectismuchmorelikelytobeobservedthen.Thishasimportantimplicationsforthemanagementofcreditriskportfolios,wheredefaultcorrelationneedstobeexplicitlymodeled.Ourconceptofcounterpartyriskhasbeenmotivatedbyaseriesofrecenteventsinwhichfirm-specificrisksfigureprominently.Severalsuchexamplesaregivenbelow:1TheSouthKoreanbankingcrisiswascommonlyattributedtonon-performingloansmadetoahandfulofchaebols(industrialconglomerates).LongTermCapitalManagement’spotentialdefaulthadimplicationsforthelikelihoodofdefaultofothermajorinvestmentbanks.ThiswasthegivenreasonfortherescueeffortledbytheFederalReserveBankofNewYorkinSeptember1998.BankersTrustrevealedits$350millionpositioninRussianassetsonAugust31,1998.Amonthlater,StandardandPoor’sdowngradeditsseniordebt.GoldmanSachscommitted$2billioninbridgeloantoUnitedPan-EuropeCommunicationsonMarch22,2000.Twomonthslater,UPC’sstockpricewasdown69percentandGoldmanSachswasunabletofindabuyerforthisloan.FirstBostonextendeda$457millionbridgeloantothepurchaserofOhioMattressin1989.ItendedupowningOhioMattressandcouldnotrecoveritsloan.ThisresultedinatakeoverbyCreditSuisse.Whiletherearenumerousstoriesliketheseinthefinancialpress,acommonthreadisthatafirmwillfacesignificantcounterpartyriskwhenitsportfolioisconcentratedinjustafewpositions.Asthesepositionschange,oftenunexpectedly,thefirmislikelytorunintofinancialdi