信贷衍生品：建模和计算(新展银行 林卫东)

信贷衍生产品：

建模和计算林卫东CreditDerivatives2024/6/16摘要引言信贷产品法规和文档(LegalandDocumentation)行业规范（Regulatoryenvironment)复杂信贷产品定价，计算技术和对冲(Hedge)风险管理2024/6/16摘要引言信贷产品法规和文档(LegalandDocumentation)行业规范（Regulatoryenvironment)复杂信贷产品定价，计算技术和对冲(Hedge)风险管理2024/6/16引言风险市场（creditriskmarket)公司债券信贷衍生产品(creditderivatives)一种能把信贷风险从基础资产中剥离出来，便于交易和管理的衍生工具基本功能： 风险有效转换，聚集，分散和重新包装2024/6/16信贷衍生产品的增长单个信贷CDS信贷指数相关性波动性Source:ISDA2024/6/16市场的参与者Source:BBA2003/2004survey2024/6/16市场的参与者2024/6/16信贷衍生产品的创新Source:BBA2003/2004survey2024/6/16交易的产品？信贷违约互换(CreditDefaultSwap,CDS)完全收益互换(TotalReturnSwap,TRS)信贷短期债券(CreditLinkedNote,CLN)信贷组合互换/债券First-to-defaultbasket,nth-to-defaultbasket信贷组合批次债券信贷产品创新Option,futures,indices,constantmaturityetc.2024/6/16市场最新发展CDSmatchingandconfirmationStandardisationofdocumentationTradableCreditfixingsMarketregulation2024/6/16摘要引言信贷产品法规和文档(LegalandDocumentation)行业规范（Regulatoryenvironment)复杂信贷产品定价，计算技术和对冲(Hedge)风险管理2024/6/16信贷违约互换(CDS)Protection买家Protection卖家银行甲银行乙某公司债券信贷溢价

creditspread违约事件发生时

100债券2024/6/16信贷短期债券(CLN)SpecialPurposeVehicle(SPV)息票+到期本金（没有违约）6%+100100（开始时）3.6%+100100（开始时）利率互换2.4%CDS2024/6/16摘要引言信贷产品法规和文档(LegalandDocumentation)行业规范（Regulatoryenvironment)复杂信贷产品定价，计算技术和对冲(Hedge)风险管理2024/6/16信贷组合第一个违约互换(FTD)Protection买家Protection卖家银行甲银行乙公司1债券……公司5债券信贷溢价

creditspread违约事件发生时

100违约债券2024/6/16SeniorClassACreditTranchedSecurities

SpecialPurposeVehicle

衍生债务抵押债券(CDO)DiversifiedPoolof,typically,fixedincomeassets

CreditRiskTransferthrough:-Cash“TrueSale”-Syntheticusing“CreditDefaultSwaps”

Assetsmaycomprise:InvestmentGradeBonds/LoansHYBondsLeveragedLoansEmergingMarketDebtABS/MBSAssetsLiabilitiesTransfer

CreditRiskTransferfor:-BalanceSheetManagement-CreditArbitrage

MezzanineClassB/C/DSubordinatedTheaboveisindicativecapitalstructureonlyAAAAAtoBBBNotRatedRatingsCDO:Collateralized“Debt”Obligations,moreencompassingtermthanothertermssuchasCBO(“Bonds”)andCLOs(“Loans”)2024/6/16衍生债务抵押债券的特点EfficientPortfolioDiversificationToolGainAccesstoAssets,OtherwiseDifficulttoAccessChooseTranchedependinguponRiskAppetiteCustomized“Portfolio”meetsInvestors’RequirementsHigherSpreadthansimilarlyRatedAssetsInvestorsreceivehigherspreadpremiumrelativetosinglenameinvestmentsforasimilarlevelofrisk2024/6/16摘要引言信贷产品法规和文档(LegalandDocumentation)行业规范（Regulatoryenvironment)复杂信贷产品定价，计算技术和对冲(Hedge)风险管理2024/6/16CDS公平溢价违约概率(p)恢复率(recoveryrate)CDS现金流FixedlegFloatinglegSSSS2024/6/16Semi-analyticModelforSTCDOnobligorsRandomvectorofdefaulttime:α1,…,αnJointDistributionandSurvivalfunctions:

F(t1,…tn)=Q(α1≤t1,…,αn

≤tn) S(t1,…tn)=Q(α1>t1,…,αn>tn) Q–pricingmeasureF1,…,Fn;S1,…,Sn;marginaldistributionandsurvivalfunctionsCopulafunctionC: F(t1,…tn)=C(F1(t1),…,Fn(tn))Ei–nominal;δi–recoveryrate;Mi=Ei*δi–lossgivendefault;AlatentfactorVsuchthatconditionallyonV,defaulttimesareindep:

pti|V=Q(αi

≤t

|V)conddefaultprob;qti|V=Q(αi

>t

|V)condsurvivalprob;Socondjointsurvivalprob: S(t1,…tn|V)=∏qtii|V

2024/6/16STCDO(continued)Aggregatedlossprocess: L(t)=∑MiNi(t) Ni(t)--defaultindicatorprocessPVofdefaultleg=E[(L(t)-K)+],whereKisthetranche’sattachmentSemi-analytictechniquesappliedforthecomputationoflossexpection

FFTandrecursiveHowtorepresentdefaulttime?2024/6/16DavidLi’s1-factormodelGaussianvector,v1,…,vn

Gaussiancdf2024/6/16StochasticCorrelationCorrelationparametersIndependentstochasticcorrelationwithdistributionfunctionF2024/6/16StudenttCopulaW----independentfromthe2ndpartandaninverseGammadistributionwithparametersequaltov/2.V,-----independentGaussianrandomvariables.----thedistributionfunctionofthestandardunivariateStudentt2024/6/16DoubletCopulaProposedrecentlybyHull&White(2004)Latentvariables:---independentt-distributionrandomvariables.---degreesoffreedomforDefaulttime:2024/6/16ClaytonCopulaConsiderapositiverandomvariableV(1-fatcor),std.GammadistributionwithShapeparameterofIndependentuniformrandomvariablesalsoindependentfromVDefaulttime.2024/6/16摘要引言信贷产品法规和文档(LegalandDocumentation)行业规范（Regulatoryenvironment)复杂信贷产品定价，计算技术和对冲(Hedge)风险管理2024/6/16市场风险管理(marketrisk)CreditVaRInterestrateriskmonitor2024/6/16信贷风险管理(creditrisk)多维性信贷风险控制信贷证券组合的风险分析2024/6/16国内金融资产结构

国内金融市场融资结构(2003)贷款3万亿(85%);直接融资5340亿(15%):股票、国债、企业债券

直接金融(200312515亿）政府债券比重：6280亿元（占比50.2％）政策性银行金融债发行4520亿元（占比36.1％）股票发行1357亿元（占比10.8％）企业债券发行量358亿元（占比2.9％）2024/6/162003年直接融资比重2024/6/1