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1、MethodolComputApplProbab(2009)11:95115DOI10.1007/s11009-007-9067-xBayesianCopulaeDistributions,withApplicationtoOperationalRiskManagementLucianaDallaValleReceived:12July2007/Revised:27November2007/Accepted:18December2007/Publishedonline:24January2008©SpringerScience+BusinessMedia,LLC2007A
2、bstractTheaimofthispaperistointroduceanewmethodologyforoperationalriskmanagement,basedonBayesiancopulae.Oneofthemainproblemsrelatedtooperationalriskmanagementisunderstandingthecomplexdependencestructureoftheassociatedvariables.Inordertomodelthisstructureinaflexibleway,weconstructamethodbas
3、edoncopulae.Thisallowsustosplitthejointmultivariateprobabilitydistributionofarandomvectoroflossesintoindividualcomponentscharacterizedbyunivariatemarginals.Thus,copulafunctionsembodyallthein-formationaboutthecorrelationbetweenvariablesandprovideausefultechniqueformodellingthedependencyofa
4、highnumberofmarginals.Anotherimportantprobleminoperationalriskmodellingisthelackoflossdata.ThissuggeststheuseofBayesianmodels,computedviasimulationmethodsand,inparticular,MarkovchainMonteCarlo.Weproposeanewmethodologyformodellingoperationalriskandforestimatingtherequiredcapital.Thismethod
5、ologycombinestheuseofcopulaeandBayesianmodels.KeywordsBayesiannormalcopula·BayesianStudentstcopula·Expectedshortfall·Lossdistributionapproach·MarkovchainMonteCarlo·Operationalrisk·ValueatriskAMS2000SubjectClassification62C10·60E05·65C05·91B301IntroductionOperationalriskistheriskoflossresul
6、tingfrominadequateorfailedinternalprocesses,peopleandsystemsorfromexternalevents(RiskManagementGroupL.DallaValle(B)DepartmentofEconomics,BusinessandStatistics,FacultyofPoliticalScience,UniversityofMilan,Milan,Italye-mail:luciana.dallavalle@unimi.it96MethodolComputApplProbab(2009)11:951152
7、003).ThisishowtheBaselCommitteeonBankingSupervision(BCBS)definesthistypeofrisk,withtheultimatepurposeofprescribingcapitaladequacystandardsforallinternationallyactivebanks(formoredetails,seeBaselCommitteeonBankingSupervision2001,2003andNash2003).Thesestandardsaregauge
