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(CDO)():10,CDO,CDOBETCopulaCopulaCDO;Copula;:CDO;;;:F830.91:A:16722884X(2008)0420616209AReview:ResearchofPricingModelsforCDOCHENTianQINXuezhi(DalianUniversityofTechnology,Dalian,Liaoning,China)Abstract:Asoneofthemostpopularcreditderivativesinthelasttenyears,CDOiswidelyap2pliedtotheriskmanagementofforeignbanksandotherfinancialinstitutions.TheinnovationandpricingofCDOandotherfinancialderivativeshavebeenpaidtocloseattentionintherecentUSsub2primecrisis.BasicCDOpricingmodelswithafocusontheBET,theCopulamodelandtheFactorCopulamodelcommonlyusedincurrentfinancialindustrywereintroducedandanalyzedsystematical2ly.BoththeFactorCopulamodeandthedynamicmodelwerereviewedbriefly.Futureresearchtrendsinthisfieldarealsopointed.Keywords:CDO;creditrisk;assetsecuritization;creditderivatives:2007210212:(70771018);(05JA630005);CDO:,,,,,CDO,,2006,CDO488CDO,200512,41.772(CDO),20064,57.2988(CDO)20079,07(CDO),43.83,CDO,2007600:10,,CDOCDO()(),(specialpurposevehi2cle,SPV),SPV,,6165420087ChineseJournalofManagementVol.5No.4Jul.20083,,,,,,,MoodyStan2dard&Poor(S&P)FitchCDO,11CDOMoodyStandard&PoorFitchBETMBETCBMCDOROMCDOEVALUATORVECTORBETCopu2laCopulaCDO,Copula,,CDO1CDOCDO:CDO,;,,,;,,,CDO,CDOCDO,,CDO,11.1BET(binomialexpansiontech2nique),BET,CIFUENTES[1],(diversityscore,DS)1CDO,(expectedloss,EL),Moody,:(1)DS1DS=mk=1Hnki=1min{1,NiöN},,m;nkk;Nii;N=ni=1Niön,n;H(x)Moody2DS=ni=1PDiNini=1(1-PDi)NiQijPDi(1-PDi)PDj(1-PDj)NiNj,,PDii;Qijij(2)PR(3)iPi=DS!i!(DS-i)!Pi(1-P)DS-i(4)iLi=iN(1-R)(5)EL=DSi=1PiLi,MoodyBET,(multi2binomialexpansiontechnique,MBET)(correlatedbinomialmethod,CBM),716(CDO):;;,,;,,1.2CopulaCopula,Copula,,DL(de2faultleg)PL(premiumleg):nCDO,F1(t1),F2(t2),,Fn(tn)(0,1)n(0,1)CopulaC(SklarC):C=(u1,u2,,un)=G[(F-11(u1),F-12(u2),,F-1n(un)],,F-1i(ui)Fi(ti),G:(1)Copula,nUi(2)UiSi,Si,K(t);Si=-lnUiöK,Si(3),CDO(i)L(t)=ni=1(1-Ri)Ni1{Sit},[#,$]L#,$(t)=[L(t)-#]1{#,$}[L(t)]+($-#)1$,ni=1Ai[L(t)],,Rii(ii)DL=ET0B(0,t)dL#,$(t),,T=tn,B(0,t)(iii)PL=Eni=1sAB(0,ti)min{max[$-L(ti),0],$-#},,s;A;L(ti)=(1-Ri)Ni(4),DLPL,,s=ET0B(0,t)dL#,$(t)Eni=1AB(0,ti)min{max[$-L(ti),0],$-#}BET,Copula,,,,,,1.3CopulaCopula,,Copula,,,,,1.3.1,Vi=QiY+1-Q2iZi,i=1,2,,n,,Vii;Y,;Zi,;QiiZi,YZi,01,YZiViF(y)H(z)Gi(v)1.3.2(1)Kii,:Si=inf{t0ViKi},i=1,2,,nipi,Ki=G-1i(pi),iYypi(y)=P(ViKiûY=y)=PziKi-QiY1-Q2iûY=y=HG-1i(pi)-Qiy1-Q2i(2)8165420087{P[L(t)=k],k=1,2,,Ni}P[Ln(t)=kûY=y],:P[Ln(t)=k]=-P(Ln(t)=kûY=y)dF(y)(3)CDO,(i)DL=B(0,T)E[LDL(T)]+T0E[LDL(t)]dB(0,t),,E[LDL(t)]=($-#)P[L(t)$]+$#(x-#)dFL(x),FLL(t)(ii)PL=ni=1B(0,ti)sA($-#)P[L(ti)#]+$#($-x)dFL(x)(ii)s=B(0,T)E[LDL(T)]+T0E[LDL(t)]dB(0,t)ni=1B(0,ti)A($-#)P[L(ti)#]+$#($-x)dFL(x)Copula,,,CopulaCDO2CDO2.1CopulaBlack&Scholes,CDOCopula(2,2,),MCGINTY[2]BaseCorrelation,,,,Copula7:(1)CopulaLI[3]GaussianCopulaCDO,StudenttClaytonMarshall2OlkinDou2bletCopulaCDO(2)2CopulaCDOLI[3],SCHONBUCHER[4]GaussianCopulaMASHAL[5],ANDERSEN[6],DEMAR2TA[7],EMBRECHTS[8],FREY[9],O’KANE[10],LINDSKOG[11],MASHAL[12],GREENBERG[13]StudenttCopulaSCHONBUCHER[4],SCHONBUCHER[14],ROGGE[15],FRIEND[16],O’KANE[10],LAURENT[17],GREGORY[18],MADAN[19]ClaytonCopulaDUFFIE[20],WONG[21],GIESECKE[22],ELOUERKHAOUI[23],LINDSKOG[11]Marshall2OlkinCopulaHULL[24]DoubletCopula43BURTSCHELL[25]CopulaCDO(34)StudenttClay2tonCopulaGaussianCopula,Marshall2OlkinDoubletCopu2la,DoubletCopulaCopula916(CDO)(2)LI[3]LAURENT[17],GREGORY[18]ANDERSEN[6]HULL[24],,,,,(3),,ANDERSEN[26],GREGORY[27]CDO,,,,(4),GREGORY[18],ANDERSEN[6]HULL[24],,GORDY[28]CDODAVIS[29]JARROWR[30],,,(5),GaussianCop2ula,Gaus2sianCopulaKALEMANOVA[31]NIG(normalinversegaussian)CDO,DoubletCopula,CDO;MOOSBRUCKER[32]VG(variancegamma)CDO,,;BRUNLID[33]SkewedStudenttCopula,PRANGE[34]CDO,(6)Copula,BURTSCHELL[35]Copula,ANDERSEN[26]RFL,TURC[36],(7)CDO,,,PYKHTIN[37]CDO,GREGORY[18],,,GaussianCopulaArchimedeanCopula,DEBUYSSCHER[38],ANDERSEN[6],HULL[24],,,,GARCHSaddle2pointEdgeworthlargedeviationsJarrow2Rudd,CopulaCopula,,,,,CDO,CDO2.2BETMBET,Copula0265420087Copula,,CDO,CDO,[3953],Bottom2up(3)Top2down(4)2Bottom2up,;Top2down,,Bottom2up23Bottom2up2005ALBANESE[39]2006BAXTER[40]levyCDO2005HULL[41]ImpliedCopula2005TOTOUOM[42]Copula2006CHAPOVSKY[43]22006GRAZIANO[44](MC)2005HURD[45](AMC)2006JOSHI[46]GAMMA4Top2down2004SIDENIUS[47]HeathJarrowMerton2005BENNANI[48]2005WALKER[49]2005SCHONBUCHER[50]Markovchain2006ERRAIS[51]2006LONGSTAFF[52]2007BRIGO[53],,,,Bottom2up,,,,CDOCDOCDO,CDOCDOTop2down,,,CDOCDO,,:,;,,;,;,;,MarkovLevy,,2.3CDO,CDO,,,:[54],ö,,,,CDO[55]Copula,,2,Copula[56]Copula,MonteCarloCDO[57],,CDO,CDO,[58]Copula,CDO,,,,126(CDO)[59]NIG,3,,[60]CDO,,,CDO[61]KMVCopula,,,,,3CDO3.1CDOCDO,CDO,:(1)CDO,,CDO,CDOCDO(2)CDO,,CDOCDSCDO(3),,CDO,,,(4)CDO,(5),3.2CDO,,,,,,CDO:(1),CDO,LEVY,GARCH,Copu2la,(2)CDOCDO,CDO,,,CDO(3),CDO,delta,(4)CDO,CDOCPPICDOCDOCDO,CDOCDO,,CDO[1]CIFUENTESA,O’CONNORG.TheBinomialEx2pensionMethodAppliedtoCBOöCLOAnalysis[R].NewYork:Moody’sInvestorService,1996.[2]MCGINTYL,BEINSTEINE,AHLUWALIAR,etal.IntroducingBaseCorrelations[R].NewYork:JPMorgan,2004.[3]LIDX.OnDefaultCorrelation:ACopulaApproach[J].JournalofFixedIncome,2000,9(4):4354.[4]SCHONBUCHERPJ,SCHUBERTD.Copula2De