信貸衍生品：建模和計算(新展銀行 林衛(wèi)東)

1、信貸衍生產(chǎn)品：信貸衍生產(chǎn)品：建模和計算建模和計算 林衛(wèi)東2022-6-30摘要摘要l引言引言l信貸產(chǎn)品信貸產(chǎn)品l法規(guī)和文檔(Legal and Documentation)l行業(yè)規(guī)范（Regulatory environment)l復雜信貸產(chǎn)品復雜信貸產(chǎn)品l定價，計算技術(shù)定價，計算技術(shù)和對沖(Hedge)l風險管理風險管理2022-6-30摘要摘要l引言引言l信貸產(chǎn)品l法規(guī)和文檔(Legal and Documentation)l行業(yè)規(guī)范（Regulatory environment)l復雜信貸產(chǎn)品l定價，計算技術(shù)和對沖(Hedge)l風險管理2022-6-30引言引言l風險市場（credit

2、 risk market)l公司債券l信貸衍生產(chǎn)品(credit derivatives)l一種能把信貸風險從基礎資產(chǎn)中剝離出來，便于交易和管理的衍生工具l基本功能：風險有效轉(zhuǎn)換，聚集，分散和重新包裝2022-6-30信貸衍生產(chǎn)品的增長信貸衍生產(chǎn)品的增長單個信貸CDS信貸指數(shù)相關(guān)性波動性Source: ISDA2022-6-30市場的參與者市場的參與者Source:BBA 2003/2004 survey2022-6-30市場的參與者市場的參與者2022-6-30信貸衍生產(chǎn)品的創(chuàng)新Source:BBA 2003/2004 survey2022-6-30交易的產(chǎn)品？交易的產(chǎn)品？l信貸違約互換(C

3、redit Default Swap, CDS)l完全收益互換(Total Return Swap, TRS)l信貸短期債券(Credit Linked Note, CLN)l信貸組合互換/債券First-to-default basket, nth-to-default basketl信貸組合批次債券l信貸產(chǎn)品創(chuàng)新Option, futures, indices, constant maturity etc.2022-6-30市場最新發(fā)展市場最新發(fā)展lCDS matching and confirmationlStandardisation of documentationlTradable

4、 Credit fixingslMarket regulation2022-6-30摘要摘要l引言引言l信貸產(chǎn)品信貸產(chǎn)品l法規(guī)和文檔(Legal and Documentation)l行業(yè)規(guī)范（Regulatory environment)l復雜信貸產(chǎn)品l定價，計算技術(shù)和對沖(Hedge)l風險管理2022-6-30信貸違約互換信貸違約互換(CDS)Protection 買家Protection 賣家銀行甲銀行乙某公司債券 信貸溢價 credit spread違約事件發(fā)生時 100債券2022-6-30信貸短期債券信貸短期債券(CLN)Special Purpose Vehicle(SPV)息

5、票+到期本金（沒有違約）6% + 100100（開始時）3.6% + 100100（開始時）利率互換2.4%CDS2022-6-30摘要摘要l引言引言l信貸產(chǎn)品l法規(guī)和文檔(Legal and Documentation)l行業(yè)規(guī)范（Regulatory environment)l復雜信貸產(chǎn)品復雜信貸產(chǎn)品l定價，計算技術(shù)和對沖(Hedge)l風險管理2022-6-30信貸組合第一個違約互換信貸組合第一個違約互換(FTD)Protection 買家Protection 賣家銀行甲銀行乙公司1債券公司5債券 信貸溢價 credit spread違約事件發(fā)生時 100違約債券2022-6-30Sen

6、ior Class ACreditTranchedSecurities SpecialPurposeVehicle 衍生債務抵押債券 (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衍生債務抵押債券的特點 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信貸產(chǎn)品l法規(guī)和文檔(Legal and Documentation)l行業(yè)規(guī)范（Regulatory environment)l復雜信貸產(chǎn)品l定價，計算技術(shù)和對沖定價，計算技術(shù)和對沖(Hedge)l風險管理2022-6-30CDS公平溢價公平溢價l違約概率(p)l恢復率(recovery rate)lCDS 現(xiàn)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信貸產(chǎn)品l法規(guī)和文檔(Legal and Documentation)l行業(yè)規(guī)范（Regulatory environment)l復雜信貸產(chǎn)品l定價

17、，計算技術(shù)和對沖(Hedge)l風險管理風險管理2022-6-30市場風險管理市場風險管理(market risk)lCredit VaRlInterest rate risk monitor2022-6-30信貸風險管理信貸風險管理(credit risk)l多維性信貸風險控制l信貸證券組合的風險分析2022-6-30國內(nèi)金融資產(chǎn)結(jié)構(gòu)國內(nèi)金融資產(chǎn)結(jié)構(gòu) l國內(nèi)金融市場融資結(jié)構(gòu)(2003)l貸款 3萬億 (85%);l直接融資 5340億(15%):股票、國債、企業(yè)債券 l直接金融 (2003 12515億）l政府債券比重 ：6280億元（占比50.2） l政策性銀行金融債發(fā)行4520億元（占比36.1） l股票發(fā)行1357億元（占比10.8） l企業(yè)債券發(fā)行量358億