credit risk under the benchmark approach

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1、Chapter14CreditRiskUndertheBenchmarkApproachInthischapter,wediscusshowtomodelcreditriskunderthebenchmarkapproach.WeemploythetechniquesfromSect.12.3inFilipovic(«2009),andweshowhowunderthebenchmarkapproach,theLaplacetransformsderivedinthisbookcanbeincorp

2、oratedinthisframework.Thestructureofthischapterisasfollows:ÞrstlyweintroduceanafÞnecreditriskmodelinSect.14.1.ThismodelsatisÞesthekeyassumptionsofSect.12.3inFilipovic(«2009).Hencetheresultspresentedthereap-ply,whichwerecallfortheconvenienceofthereader.

3、Consequently,inSect.14.2,weshowhowtopricecreditdefaultswaps(CDSs)andintroducecreditvaluationadjustment(CVA)inSect.14.3asanextensionofCDSs.Inparticular,ourmodelcancaptureright-wayÑandwrong-wayexposure.Thismeans,wecapturethede-pendencestructureofthedefau

4、lteventandthevalueofthetransactionundercon-sideration.Forsimplecontracts,weprovideclosed-formsolutions,however,duetothefactthatweallowforadependencebetweenthedefaulteventandthevalueofthetransaction,closed-formsolutionsaredifÞculttoobtainingeneral.Hence

5、weconcludethischapterwithareducedformmodel,whichismoretractablethanthemodelfromSect.14.1.14.1AnAffineCreditRiskModelInthissection,weaimtointroducearealistic,yettractablemodelforcreditrisk.Inparticular,ourmodelallowsforastochasticinterestrate,andastochas

6、ticdefaultintensity,bothofwhicharecorrelatedwiththeGOP.Mathematically,themodelisbasedontheapproachinSect.12.3inFilipovic(«2009).WepointoutthatourmodelsatisÞestheassumptions(D1)and(D2),seepages230and233inFilipovic«(2009),andhencewecanemploytheresultspre

7、sentedinthisreference.Forfurthertechnicalbackground,wereferthereadertothisreference.WeÞxaprobabilityspace(Ω,A,P),wherePdenotestherealworldprobabilitymeasure.Next,wepresentamodelfortheevolutionofÞnancialinformation.Weremarkthatinourmodel,onlyhavingacces

8、stomarketinformationisnotsufÞcientJ.Baldeaux,E.Platen,FunctionalsofMultidimensionalDiffusionswithApplications343toFinance,Bocconi&SpringerSeries5,DOI10.1007/978-3-319-00747-2_14,©SpringerInternationalPublishingSwitzerland201334414Credit