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1、MathematicalFinance,Vol.24,No.1(January2014),125146ARBITRAGE-FREEBILATERALCOUNTERPARTYRISKVALUATIONUNDERCOLLATERALIZATIONANDAPPLICATIONTOCREDITDEFAULTSWAPSDAMIANOBRIGODepartmentofMathematics,KingsCollegeAGOSTINOCAPPONISchoolofIndustrialEngineering,PurdueUniversity
2、ANDREAPALLAVICINIBancaIMIWedevelopanarbitrage-freevaluationframeworkforbilateralcounterpartyrisk,wherecollateralisincludedwithpossiblerehypothecation.Weshowthattheadjust-mentisgivenbythesumoftwooptionpayoffterms,whereeachtermdependsonthenettedexposure,i.e.,thediff
3、erencebetweentheon-defaultexposureandthepredefaultcollateralaccount.Wethenspecializeouranalysistocreditdefaultswaps(CDS)asun-derlyingportfolios,andconstructanumericalschemetoevaluatetheadjustmentunderadoublystochasticdefaultframework.Inparticular,weshowthatforCDSc
4、ontractsaperfectcollateralizationcannotbeachieved,evenundercontinuouscollateralization,ifthereferenceentitysandcounterpartysdefaulttimesaredependent.Theimpactofrehypothecation,collateralmarginingfrequency,anddefaultcorrelation-inducedcontagionisillustratedwithnume
5、ricalexamples.Keywords:counterpartyrisk,CVA,bilateralCVA,arbitrage-freecreditvaluationadjustment,creditdefaultswaps,creditspreadvolatility,defaultcorrelation,contagion,stochasticintensity,collateralmargining,netting,rehypotecation,wrongwayrisk.1.INTRODUCTIONCounte
6、rpartycreditriskhasproventobeoneofthemajordriversofthecreditcrisis,duethehighnumberofcreditqualitydeteriorationsanddefaulteventsexperiencedbyseveral?nancialentities.Werecallasafundamentalexamplethesevencrediteventsthatoccurredinonemonthof2008,involvingFannieMae,Fr
7、eddieMac,LehmanBrothers,WashingtonMutual,Landsbanki,Glitnir,andKaupthing.Furthermore,theBIS(2011)noticesthatUnderBaselII,theriskofcounterpartydefaultandcreditmigrationriskwereaddressedbutmark-to-marketlossesduetocreditvaluationadjustments(CVA)werenot.Duringthe?nan
8、cialcrisis,however,roughlytwo-thirdsoflossesattributedtocounterpartycreditriskwereduetoCVAlossesandonlyaboutone-thirdwereduetoactualdefaults.Thispaperis
