信贷衍生品：建模和计算(新展银行 林卫东)

1、信贷衍生产品：信贷衍生产品：建模和计算建模和计算 林卫东2022-6-30摘要摘要l引言引言l信贷产品信贷产品l法规和文档(Legal and Documentation)l行业规范（Regulatory environment)l复杂信贷产品复杂信贷产品l定价，计算技术定价，计算技术和对冲(Hedge)l风险管理风险管理2022-6-30摘要摘要l引言引言l信贷产品l法规和文档(Legal and Documentation)l行业规范（Regulatory environment)l复杂信贷产品l定价，计算技术和对冲(Hedge)l风险管理2022-6-30引言引言l风险市场（credit

2、 risk market)l公司债券l信贷衍生产品(credit derivatives)l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l基本功能：风险有效转换，聚集，分散和重新包装2022-6-30信贷衍生产品的增长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: ISDA2022-6-30市场的参与者市场的参与者Source:BBA 2003/2004 survey2022-6-30市场的参与者市场的参与者2022-6-30信贷衍生产品的创新Source:BBA 2003/2004 survey2022-6-30交易的产品？交易的产品？l信贷违约互换(C

3、redit Default Swap, CDS)l完全收益互换(Total Return Swap, TRS)l信贷短期债券(Credit Linked Note, CLN)l信贷组合互换/债券First-to-default basket, nth-to-default basketl信贷组合批次债券l信贷产品创新Option, futures, indices, constant maturity etc.2022-6-30市场最新发展市场最新发展lCDS matching and confirmationlStandardisation of documentationlTradable

4、 Credit fixingslMarket regulation2022-6-30摘要摘要l引言引言l信贷产品信贷产品l法规和文档(Legal and Documentation)l行业规范（Regulatory environment)l复杂信贷产品l定价，计算技术和对冲(Hedge)l风险管理2022-6-30信贷违约互换信贷违约互换(CDS)Protection 买家Protection 卖家银行甲银行乙某公司债券 信贷溢价 credit spread违约事件发生时 100债券2022-6-30信贷短期债券信贷短期债券(CLN)Special Purpose Vehicle(SPV)息

5、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%CDS2022-6-30摘要摘要l引言引言l信贷产品l法规和文档(Legal and Documentation)l行业规范（Regulatory environment)l复杂信贷产品复杂信贷产品l定价，计算技术和对冲(Hedge)l风险管理2022-6-30信贷组合第一个违约互换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 credit spread违约事件发生时 100违约债券2022-6-30Sen

6、ior Class ACreditTranchedSecurities SpecialPurposeVehicle 衍生债务抵押债券 (CDO)Diversified Pool of , typically, fixed income assets Credit Risk Transfer through: - Cash “True Sale” - Synthetic using “Credit Default Swaps” Assets may comprise: Investment Grade Bonds / Loans HY Bonds Leveraged Loans Emerging

7、 Market Debt ABS / MBSAssetsLiabilitiesTransfer Credit Risk Transfer for: - Balance Sheet Management - Credit Arbitrage Mezzanine Class B/C/DSubordinatedThe above is indicative capital structure onlyAAAAA toBBBNotRatedRatingsCDO : Collateralized “Debt” Obligations, more encompassingterm than other t

8、erms such as CBO (“Bonds”) and CLOs (“Loans”)2022-6-30衍生债务抵押债券的特点 Efficient Portfolio Diversification Tool Gain Access to Assets, Otherwise Difficult to Access Choose Tranche depending upon Risk Appetite Customized “Portfolio” meets Investors Requirements Higher Spread than similarly Rated Assets In

9、vestors receive higher spread premium relative to single name investments for a similar level of risk2022-6-30摘要摘要l引言引言l信贷产品l法规和文档(Legal and Documentation)l行业规范（Regulatory environment)l复杂信贷产品l定价，计算技术和对冲定价，计算技术和对冲(Hedge)l风险管理2022-6-30CDS公平溢价公平溢价l违约概率(p)l恢复率(recovery rate)lCDS 现金流Fixed legFloating leg

10、SSSSiiniiiniiidfprdfppiniiiiiniiSNrdfppNSdfp111)1()(111)1 ()()1 (2022-6-30Semi-analytic Model for STCDOln obligorslRandom vector of default time: 1, nlJoint Distribution and Survival functions:F(t1,tn)=Q(1t1, n tn)S(t1,tn)=Q(1t1, n tn)Q pricing measurelF1,Fn; S1,Sn; marginal distribution and surviva

11、l functionslCopula function C: F(t1,tn)=C(F1(t1), , Fn(tn)lEi nominal; i recovery rate; Mi = Ei * i loss given default;lA latent factor V such that conditionally on V, default times are indep:pti|V = Q(i t | V) cond default prob; qti|V = Q(i t | V) cond survival prob; So cond joint survival prob:S(t

12、1,tn | V)= qtii|V 2022-6-30STCDO (continued)lAggregated loss process:L(t) = Mi Ni(t)Ni(t) - default indicator processlPV of default leg = E (L(t)-K)+ , where K is the tranches attachmentlSemi-analytic techniques applied for the computation of loss expection FFT and recursivelHow to represent default

13、 time?2022-6-30David Lis 1-factor modellGaussian vector, v1, , vniiVVv21)(1iiivF)(211)(|tFVVitipGaussian cdf2022-6-30Stochastic Correlation)1)(1 ()1(22iiiiiVVBVVBviiiiiiVBBVBBv2)1 (1)1 (iB10iiiiVVv21iIndependent stochastic correlation with distribution function F101)(|)()(21dFptFVViti2022-6-30Studen

14、t t Copula)1(2iiVVWv)(212/11)(,|tFtWVWVitivp)(1iviivtFW - independent from the 2nd part and an inverse Gamma distribution with parameters equal to v/2.V, - independent Gaussian random variables.iVvt- the distribution function of the standard univariate Student t2022-6-30Double t CopulalProposed rece

15、ntly by Hull & White (2004)lLatent variables:nvv ,1ivvvviVVv2/1222/12)(1)()(22/1211)()(2/12|VtFHvvvVitvviitpiVV ,vv,- independent t-distribution random variables.- degrees of freedom for iVV ,)(1iiiivHFDefault time:2022-6-30Clayton Copula0,1transformLaplacexxexfx0,)(/ )1()/1(1Consider a positive

16、 random variable V (1-fatcor), std. Gamma distribution withShape parameter of )(1(exp(),()()1()()(|1ln0/1tFVpVFUvsdxexfsiVitiiiiVUisxiIndependent uniform random variables also independent from VDefault time.2022-6-30摘要摘要l引言引言l信贷产品l法规和文档(Legal and Documentation)l行业规范（Regulatory environment)l复杂信贷产品l定价

17、，计算技术和对冲(Hedge)l风险管理风险管理2022-6-30市场风险管理市场风险管理(market risk)lCredit VaRlInterest rate risk monitor2022-6-30信贷风险管理信贷风险管理(credit risk)l多维性信贷风险控制l信贷证券组合的风险分析2022-6-30国内金融资产结构国内金融资产结构 l国内金融市场融资结构(2003)l贷款 3万亿 (85%);l直接融资 5340亿(15%):股票、国债、企业债券 l直接金融 (2003 12515亿）l政府债券比重 ：6280亿元（占比50.2） l政策性银行金融债发行4520亿元（占比36.1） l股票发行1357亿元（占比10.8） l企业债券发行量358亿