信用风险和资产证券化衍生品定价方法介绍_第二部分-信用和资产证券化衍生品定价

1、金融工程案例分析课程， George Yuan， 2013-14第二部分第二部分信用和资产证券化衍生品定价信用和资产证券化衍生品定价1金融工程案例分析课程， George Yuan， 2013-142第一部分第一部分: 信用风险理论介绍（信用风险理论介绍（2014年年7日上午日上午9:00am-11:30am）第第1章信用风险介绍和信用评级章信用风险介绍和信用评级第第2章章Merton 信用风险模型信用风险模型, KMV等模型应用介绍等模型应用介绍第第3章信用风险价值量调整章信用风险价值量调整(CVA)介绍介绍第第4章单因子结构模型和信用风险价值量章单因子结构模型和信用风险价值量(Credit

2、 VaR) 介绍介绍 第二部分第二部分: 信用和资产证券化衍生品定价信用和资产证券化衍生品定价( (2014年年7日下午日下午2:30pm-5:00pm) 第第1章章: 信用互换衍生品（信用互换衍生品（CDS）定价介绍）定价介绍第第2章章: 资产证券化衍生品介绍资产证券化衍生品介绍第第3章章: 资产证券化衍生品定价资产证券化衍生品定价中南财大讲学大纲中南财大讲学大纲 信用风险和资产证券化衍生品定价方法介绍信用风险和资产证券化衍生品定价方法介绍袁先智（同济大学风险管理研究所）金融工程案例分析课程， George Yuan， 2013-143 第二部分第二部分: 信用和资产证券化衍生品定价信用和资

3、产证券化衍生品定价( (2014年年7日下午日下午2:30pm-5:00pm) 第第1章章: 信用互换衍生品（信用互换衍生品（CDS）定价介绍）定价介绍第第2章章: 资产证券化衍生品介绍资产证券化衍生品介绍第第3章章: 资产证券化衍生品定价资产证券化衍生品定价中南财大讲学大纲中南财大讲学大纲 信用风险和资产证券化衍生品定价方法介绍信用风险和资产证券化衍生品定价方法介绍袁先智（同济大学风险管理研究所）金融工程案例分析课程， George Yuan， 2013-144 第二部分第二部分: 信用和资产证券化衍生品定价信用和资产证券化衍生品定价( (2014年年7日下午日下午2:30pm-5:00pm

4、) 第第1章章: 信用互换衍生品（信用互换衍生品（CDS）定价介绍）定价介绍第第2章章: 资产证券化衍生品介绍资产证券化衍生品介绍第第3章章: 资产证券化衍生品定价资产证券化衍生品定价中南财大讲学大纲中南财大讲学大纲 信用风险和资产证券化衍生品定价方法介绍信用风险和资产证券化衍生品定价方法介绍袁先智（同济大学风险管理研究所）金融工程案例分析课程， George Yuan， 2013-145Credit Default Swaps Buyer of the instrument acquires protection from the seller against a default by a

5、particular company or country (the reference entity)Example: Buyer pays a premium of 90 bps per year for $100 million of 5-year protection against company XPremium is known as the credit default spread. It is paid for life of contract or until defaultIf there is a default, the buyer has the right to

6、 sell bonds with a face value of $100 million issued by company X for $100 million (Several bonds are typically deliverable)5金融工程案例分析课程， George Yuan， 2013-14CDS Structure (Figure 24.1, page 549) 6Default Protection Buyer, ADefault Protection Seller, B90 bps per yearPayoff if there is a default by re

7、ference entity=100(1-R)Recovery rate, R, is the ratio of the value of the bond issued by reference entity immediately after default to the face value of the bond金融工程案例分析课程， George Yuan， 2013-14Other DetailsPayments are usually made quarterly in arrearsIn the event of default there is a final accrual

8、 payment by the buyerSettlement can be specified as delivery of the bonds or (more usually) in cashAn auction process usually determines the payoffSuppose payments are made quarterly in the example just considered. What are the cash flows if there is a default after 3 years and 1 month and recovery

9、rate is 40%?7金融工程案例分析课程， George Yuan， 2013-14Attractions of the CDS MarketAllows credit risks to be traded in the same way as market risksCan be used to transfer credit risks to a third partyCan be used to diversify credit risks 8金融工程案例分析课程， George Yuan， 2013-14Using a CDS to Hedge a Bond Position P

10、ortfolio consisting of a 5-year par yield corporate bond that provides a yield of 6% and a long position in a 5-year CDS costing 100 basis points per year is (approximately) a long position in a riskless instrument paying 5% per yearThis shows that bond yield spreads (measured relative to LIBOR) sho

11、uld be close to CDS spreads9金融工程案例分析课程， George Yuan， 2013-14Valuation Example (page 551-554)Conditional on no earlier default a reference entity has a (risk-neutral) probability of default of 2% in each of the next 5 years. Assume payments are made annually in arrears, that defaults always happen ha

12、lf way through a year, and that the expected recovery rate is 40%Suppose that the breakeven CDS rate is s per dollar of notional principal10金融工程案例分析课程， George Yuan， 2013-14Unconditional Default and Survival Probabilities (Table 24.1)11Time (years)Default ProbabilitySurvivalProbability10.02000.980020

13、.01960.960430.01920.941240.01880.922450.01840.9039金融工程案例分析课程， George Yuan， 2013-14Calculation of PV of Payments(Table 24.2 Principal=$1)12Time (yrs)Survival ProbExpected PaymentDiscount FactorPV of Exp Pmt10.98000.9800s0.95120.9322s20.96040.9604s0.90480.8690s30.94120.9412s0.86070.8101s40.92240.9224s

14、0.81870.7552s50.90390.9039s0.77880.7040sTotal4.0704s金融工程案例分析课程， George Yuan， 2013-1413Present Value of Expected Payoff (Table 24.3; Principal = $1)13Time (yrs)Default Probab.Rec. Rate Expected PayoffDiscount FactorPV of Exp. Payoff0.50.02000.40.01200.97530.01171.50.01960.40.01180.92770.01092.50.0192

15、0.40.01150.88250.01023.50.01880.40.01130.83950.00954.50.01840.40.01110.79850.0088Total0.0511金融工程案例分析课程， George Yuan， 2013-14PV of Accrual Payment Made in Event of a Default. (Table 24.4; Principal = $1)14TimeDefault ProbExpected Accr PmtDisc FactorPV of Pmt0.50.02000.0100s0.97530.0097s1.50.01960.009

16、8s0.92770.0091s2.50.01920.0096s0.88250.0085s3.50.01880.0094s0.83950.0079s4.50.01840.0092s0.79850.0074sTotal0.0426s金融工程案例分析课程， George Yuan， 2013-14Putting it all togetherPV of expected payments is 4.0704s + 0.0426s = 4.1130sThe breakeven CDS spread is given by4.1130s = 0.0511 or s = 0.0124 (124 bps)T

17、he value of a swap negotiated some time ago with a CDS spread of 150bps would be 4.11300.01500.0511 = 0.0106per dollar of the principal.15金融工程案例分析课程， George Yuan， 2013-14Implying Default Probabilities from CDS spreadsSuppose that the mid market spread for a 5 year newly issued CDS is 100bps per year

18、We can reverse engineer our calculations to conclude that the conditional default probability is 1.61% per year.If probabilities are implied from CDS spreads and then used to value another CDS the result is not sensitive to the recovery rate providing the same recovery rate is used throughout16金融工程案

19、例分析课程， George Yuan， 2013-14Binary CDS (page 554)The payoff in the event of default is a fixed cash amountIn our example the PV of the expected payoff for a binary swap is 0.0852 and the breakeven binary CDS spread is 207 bps17金融工程案例分析课程， George Yuan， 2013-14Credit IndicesCDX NA IG is a portfolio of

20、125 investment grade companies in North AmericaiTraxx Europe is a portfolio of 125 European investment grade namesThe portfolios are updated on March 20 and Sept 20 each yearThe index can be thought of as the cost per name of buying protection against all 125 names18金融工程案例分析课程， George Yuan， 2013-141

21、9The Use of Fixed CouponsIncreasingly CDSs and CDS indices trade like bonds to facilitate tradingA coupon is specifiedIf spread is greater than coupon, the buyer of protection pays Notional Principal Duration (SpreadCoupon)Otherwise the seller of protection pays Notional Principal Duration (CouponSp

22、read)Duration is the amount the spread has to be multiplied by to get the PV of spread payments19金融工程案例分析课程， George Yuan， 2013-1420CDS Forwards and Options (page 557-558)Example: Forward contract to buy 5 year protection on Ford for 280 bps in one year. If Ford defaults during the one-year life the

23、forward contract ceases to existExample: European option to buy 5 year protection on Ford for 280 bps in one year. If Ford defaults during the one-year life of the option, the option is knocked out 20金融工程案例分析课程， George Yuan， 2013-14Basket CDS (page 558)Similar to a regular CDS except that several re

24、ference entities are specified In a first to default swap there is a payoff when the first entity defaultsSecond, third, and nth to default deals are defined similarlyWhy does pricing depends on default correlation?21金融工程案例分析课程， George Yuan， 2013-14Total Return Swap (page 558-559)Agreement to exchan

25、ge total return on a portfolio of assets for LIBOR plus a spreadAt the end there is a payment reflecting the change in value of the assetsUsually used as financing tools by companies that want exposure to assets22 Total ReturnPayerTotal Return ReceiverTotal Return on AssetsLIBOR plus 25bps金融工程案例分析课程

26、， George Yuan， 2013-1423 第二部分第二部分: 信用和资产证券化衍生品定价信用和资产证券化衍生品定价( (2014年年7日下午日下午2:30pm-5:00pm) 第第1章章: 信用互换衍生品（信用互换衍生品（CDS）定价介绍）定价介绍第第2章章: 资产证券化衍生品介绍资产证券化衍生品介绍第第3章章: 资产证券化衍生品定价资产证券化衍生品定价中南财大讲学大纲中南财大讲学大纲 信用风险和资产证券化衍生品定价方法介绍信用风险和资产证券化衍生品定价方法介绍袁先智（同济大学风险管理研究所）金融工程案例分析课程， George Yuan， 2013-14Asset Backed Se

27、curities2425What is Wrong? 金融工程案例分析课程， George Yuan， 2013-14251)The Pricing of CDO is wrong2) The Credit Rating for CDO is wrong! (indeed wrong theory used for the CDO credit rating)No-Arbitrage Condition -关于关于CDO信用评级理论的建立问题信用评级理论的建立问题26Hull and White (2012) show that (1) The probability-of-default c

28、riterion used by S&P and Fitch does not satisfy the no-arbitrage condition.(2) The EL criterion used by Moodys does satisfy the no-arbitrage condition. However, the EL alone is not necessary correct : CRAs calculate EL in the real world (P-measure), not in the risk-neutral world (Q-measure).Ratings

29、and bond yields as well as default correlation are the main concern. Understanding corporate debts from prices to default and default correlation responding to rating is an challenge problem.Duan and van Laere (2012) indicate that having more nuanced credit information instead of a simple letter gra

30、de will itself be a major step forward in credit rating reform.WThe Credit Crisis of 200727Credit_VaR_Summary, George_Yuan 2013-2014U.S. Real Estate Prices, 1987 to 2011: S&P/Case-Shiller Composite-10 Index28Credit_VaR_Summary, George_Yuan 2013-2014What happenedStarting in 2000, mortgage originators

31、 in the US relaxed their lending standards and created large numbers of subprime first mortgages. This, combined with very low interest rates, increased the demand for real estate and prices rose. To continue to attract first time buyers and keep prices increasing they relaxed lending standards furt

32、her Features of the market: 100% mortgages, ARMs, teaser rates, NINJAs, liar loans, non-recourse borrowing29Credit_VaR_Summary, George_Yuan 2013-2014What happened.Mortgages were packaged in financial products and sold to investorsBanks found it profitable to invest in the AAA rated tranches because

33、the promised return was significantly higher than the cost of funds and capital requirements were lowIn 2007 the bubble burst. Some borrowers could not afford their payments when the teaser rates ended. Others had negative equity and recognized that it was optimal for them to exercise their put opti

34、ons.U.S. real estate prices fell and products, created from the mortgages, that were previously thought to be safe began to be viewed as riskyThere was a “flight to quality” and credit spreads increased to very high levels30Credit_VaR_Summary, George_Yuan 2013-2014Asset Backed Security (Simplified)

35、A “waterfall” defines the precise rules for allocating cash flows to tranchesAsset 1Asset 2Asset 3Asset nPrincipal:$100 million SPVSenior TranchePrincipal: $75 millionReturn = 6%Mezzanine TranchePrincipal:$20 millionReturn = 10%Equity Tranche Principal: $5 millionReturn =30%31Credit_VaR_Summary, Geo

36、rge_Yuan 2013-2014ABSThe WaterfallEquity TrancheSenior TrancheMezzanine TrancheAsset Cash Flows32Credit_VaR_Summary, George_Yuan 2013-2014ABS CDOs or Mezz CDOs (Simplified)Subprime MortgagesSenior Tranches (75%)AAAMezzanine Tranches (20%)BBBEquity Tranches (5%)Not RatedSenior Tranche (75%)AAAMezzani

37、ne Tranche (20%) BBBEquity Tranche (5%)How much of the original portfolio of subprime mortgages is AAA?33Credit_VaR_Summary, George_Yuan 2013-2014 ABSs ABS CDOLosses to AAA Tranche of ABS CDO (Table 6.1)Losses on Subprime portfoliosLosses on Mezzanine Tranche of ABSLosses on Equity Tranche of ABS CD

38、OLosses on Mezzanine Tranche of ABS CDOLosses on Senior Tranche of ABS CDO10%25%100%100%0%15%50%100%100%33.3%20%75%100%100%66.7%25%100%100%100%100%34Credit_VaR_Summary, George_Yuan 2013-2014A More Realistic Structure (Figure 6.5)Subprime MortgagesAAAAAABBBBB, NRSenior AAAJunior AAAAAABBBNRSenior AAA

39、Junior AAAAAABBBNRSenior AAAJunior AAAAAABBBNR81%11%4%3%1% ABSHigh Grade ABS CDOMezz ABS CDOCDO of CDO62%14%8%6%6%4%88% 5%3%2%1%1%60% 27%4%3%3%2%35Credit_VaR_Summary, George_Yuan 2013-2014BBB TranchesBBB tranches of ABSs were often quite thin (1% wide)This means that they have a quite different loss

40、 distribution from BBB bonds and should not be treated as equivalent to BBB bonds They tend to be either safe or completely wiped out (cliff risk)What does this mean for the tranches of the Mezz ABS CDO?Credit_VaR_Summary, George_Yuan 2013-201436Regulatory ArbitrageCapital required for securities cr

41、eated from a portfolio of mortgages was considerably less than capital that would be required if mortgages had been kept on the balance sheetCredit_VaR_Summary, George_Yuan 2013-201437Role of IncentivesArguably the incentives of valuers, the creators of ABSs and ABS CDOs, and rating agencies helped

42、to create the crisisCompensation plans of traders created short-term horizons for decision making Credit_VaR_Summary, George_Yuan 2013-201438Importance of TransparencyABSs and ABS CDOs were complex inter-related productsOnce the AAA rated tranches were perceived as risky they became very difficult t

43、o trade because investors realized they did not understand the risksOther credit related products with simpler structures (eg, credit default swaps) continued to trade during the crisis. 39Credit_VaR_Summary, George_Yuan 2013-2014Lessons from the Crisis (page 133-134)Beware irrational exuberanceDo n

44、ot underestimate default correlations in stressed marketsRecovery rate depends on default rate Compensation structures did not create the right incentivesIf a deal seems too good to be true (eg, a AAA earning LIBOR plus 100 bp) it probably isDo not rely on ratingsTransparency is important in financi

45、al marketsResecuritization was a badly flawed ideaCredit_VaR_Summary, George_Yuan 2013-201440What is Wrong? 金融工程案例分析课程， George Yuan， 2013-14411)The Pricing of CDO is wrong2) The Credit Rating for CDO is wrong! (indeed wrong theory used for the CDO credit rating)Asset Backed Securities金融工程案例分析课程， Geo

46、rge Yuan， 2013-14421 Cash CDO: 现金现金CDO2 Synthetic CDO: 合成合成 CDOAsset Backed SecuritiesSecurities created from a portfolio of loans, bonds, credit card receivables, mortgages, auto loans, aircraft leases, music royalties, etcUsually the income from the assets is tranched A “waterfall” defines how inc

47、ome is first used to pay the promised return to the senior tranche, then to the next most senior tranche, and so on.金融工程案例分析课程， George Yuan， 2013-1443The Waterfall44Equity Tranche ( no rating )Senior Tranche (AAA)Mezzanine Tranche (BBB)Asset Cash FlowsCrediting Rating Principle: 考虑2个因素： 1）对于利息利息部分，从

48、上到下。 2）对于本金本金部分，从上到下 。 ABS CDOs or Mezz CDOs (Simplified）45AssetsSenior Tranche (80%)AAAMezzanine Tranche (15%)BBBEquity Tranche (5%)Not RatedSenior Tranche (65%)AAAMezzanine Tranche (25%) BBBEquity Tranche (10%)The mezzanine tranche is repackaged with other mezzanine tranchesLosses on Subprime port

49、foliosLosses on Mezzanine Tranche of ABSLosses on Equity Tranche of ABS CDOLosses on Mezzanine Tranche of ABS CDOLosses on Senior Tranche of ABS CDO10%33.3%100%93.3%0%13%53.3%100%100%28.2%17%80.0%100%100%69.2%20%100%100%100%100%Plus Systematic RiskNo-Arbitrage Condition -关于关于CDO信用评级理论的建立问题信用评级理论的建立问

50、题46Hull and White (2012) show that (1) The probability-of-default criterion used by S&P and Fitch does not satisfy the no-arbitrage condition.(2) The EL criterion used by Moodys does satisfy the no-arbitrage condition. However, the EL alone is not necessary correct : CRAs calculate EL in the real wo

51、rld (P-measure), not in the risk-neutral world (Q-measure).Ratings and bond yields as well as default correlation are the main concern. Understanding corporate debts from prices to default and default correlation responding to rating is an challenge problem.Duan and van Laere (2012) indicate that ha

52、ving more nuanced credit information instead of a simple letter grade will itself be a major step forward in credit rating reform.W金融工程案例分析课程， George Yuan， 2013-14Collateralized Debt Obligations (Page 559-560)A cash CDO is an ABS where the underlying assets are debt obligationsA synthetic CDO involv

53、es forming a similar structure with short CDS contractsIn a synthetic CDO most junior tranche bears losses first. After it has been wiped out, the second most junior tranche bears losses, and so on47Asset Backed Securities金融工程案例分析课程， George Yuan， 2013-14481 Cash CDO: 现金现金CDO2 Synthetic CDO: 合成合成 CDO

54、 The motivation of Synthetic CDO The Motivation for Synthetic CDO (In page 400): If CDS reference is some companys “Debt”, then Long position in “Debt” is equivalent to the “Short position” of CDS (i.e., the seller of CDS), why ?金融工程案例分析课程， George Yuan， 2013-1449金融工程案例分析课程， George Yuan， 2013-14Synth

55、etic CDO Example50Page 401Page 401Synthetic CDO- Synthetic CDO- 合成合成CDO ExampleCDO ExampleTotalTotal一亿一亿RatioRatioReturn Return SpreadSpreadOne Year One Year PaymentPaymentCDSCDS 基基本本SpreadSpreadSeniorSenior 80,000,000 80.00%0.10% 80,000.00 MezzannieMezzannie 15,000,000 15.00%1% 150,000.00 Junior/Eq

56、uity Junior/Equity 5,000,000 5.00%10% 500,000.00 Total Sum 100,000,000 100.00% 730,000 0.730%0.730%金融工程案例分析课程， George Yuan， 2013-145151合成合成CDO Example金融工程案例分析课程， George Yuan， 2013-145252合成合成CDO Example金融工程案例分析课程， George Yuan， 2013-1453Synthetic CDO DetailsThe income is paid on the remaining tranche

57、principal. Example: when losses have reached 8% of the total principal underlying the CDSs, tranche 1 has been wiped out, tranche 2 earns the promised spread (200 basis points) on 80% of its principal53金融工程案例分析课程， George Yuan， 2013-1454Single Tranche TradingThis involves trading tranches of portfoli

58、os of CDSs without actually forming the portfoliosCash flows are calculated in the same way as they would be if the portfolios had been formed 54金融工程案例分析课程， George Yuan， 2013-1455Quotes for Standard Tranches of iTraxx (Table 24.6)55Quotes are 30/360 in basis points per year except for the 0-3% tranc

59、he where the quote equals the percent of the tranche principal that must be paid upfront in addition to 500 bps per year. iTraxx-Date0-3%3-7%7-10%10-15%15-30%30-100%IndexJan 1, 200710.34% 41.59 11.95 5.60 2.00 23Jan 1, 200830.98% 316.90212.40140.0073.60 77Jan 1, 200964.28%1185.63606.69315.6397.13165

60、CDX NA IGTranche0-3%3-6%6-9%9-12%12-22%22-100%iTtraxx Tranche0-3%3-7%7-10%10-15%15-30%30-100%金融工程案例分析课程， George Yuan， 2013-1456 Example for CDX Index-Page 156Example CDX.NA.IG.20金融工程案例分析课程， George Yuan， 2013-1457 Example for CDX Index-Page 257Example CDX.NA.IG.20金融工程案例分析课程， George Yuan， 2013-1458 Ex