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1、Chapter14CreditRiskUndertheBenchmarkApproachInthischapter,wediscusshowtomodelcreditriskunderthebenchmarkapproach.WeemploythetechniquesfromSect.12.3inFilipovic(?2009),andweshowhowunderthebenchmarkapproach,theLaplacetransformsderivedinthisbookcanbeincorp
2、oratedinthisframework.Thestructureofthischapterisasfollows:TrstlyweintroduceanafTnecreditriskmodelinSect.14.1.ThismodelsatisTesthekeyassumptionsofSect.12.3inFilipovic(?2009).Hencetheresultspresentedthereap-ply,whichwerecallfortheconvenienceofthereader.
3、Consequently,inSect.14.2,weshowhowtopricecreditdefaultswaps(CDSs)andintroducecreditvaluationadjustment(CVA)inSect.14.3asanextensionofCDSs.Inparticular,ourmodelcancaptureright-way?andwrong-wayexposure.Thismeans,wecapturethede-pendencestructureofthedefau
4、lteventandthevalueofthetransactionundercon-sideration.Forsimplecontracts,weprovideclosed-formsolutions,however,duetothefactthatweallowforadependencebetweenthedefaulteventandthevalueofthetransaction,closed-formsolutionsaredifTculttoobtainingeneral.Hence
5、weconcludethischapterwithareducedformmodel,whichismoretractablethanthemodelfromSect.14.1.14.1AnAf?neCreditRiskModelInthissection,weaimtointroducearealistic,yettractablemodelforcreditrisk.Inparticular,ourmodelallowsforastochasticinterestrate,andastochas
6、ticdefaultintensity,bothofwhicharecorrelatedwiththeGOP.Mathematically,themodelisbasedontheapproachinSect.12.3inFilipovic(?2009).WepointoutthatourmodelsatisTestheassumptions(D1)and(D2),seepages230and233inFilipovic?(2009),andhencewecanemploytheresultspre
7、sentedinthisreference.Forfurthertechnicalbackground,wereferthereadertothisreference.WeTxaprobabilityspace(Ω,A,P),wherePdenotestherealworldprobabilitymeasure.Next,wepresentamodelfortheevolutionofTnancialinformation.Weremarkthatinourmodel,onlyhavingacces
8、stomarketinformationisnotsufTcientJ.Baldeaux,E.Platen,FunctionalsofMultidimensionalDiffusionswithApplications343toFinance,Bocconi&SpringerSeries5,DOI10.1007/978-3-319-00747-2_14,?SpringerInternationalPublishingSwitzerland201334414Credit