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金融工程案例分析课程， George Yuan， 2013-14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1章信用风险介绍和信用评级第2章Merton 信用风险模型, KMV等模型应用介绍第3章信用风险价值量调整(CVA)介绍第4章单因子结构模型和信用风险价值量(Credit VaR) 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

2、午2:30pm-5:00pm) 第1章: 信用互换衍生品（CDS）定价介绍第2章: 资产证券化衍生品介绍第3章: 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， 2013-14 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( (2014年年7日下午日下午2:30pm-5:00pm) 第1章: 信用互换衍生品（CDS）定价介绍第2章: 资产证券化衍生品介绍第3章: 资产证券化衍生品定价中南财大讲学大纲中南财

3、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， 2013-14 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( (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2章: 资产证券化衍生品介绍第3章: 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

4、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 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

5、 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 sell bonds with a face value of $100 million issued by company X for $100 million (Several bonds are typically deliverable)金融工程案例分析课程， George Yuan， 2013-14CDS Struct

6、ure (Figure 24.1, page 549) Default Protection Buyer, ADefault Protection Seller, B90 bps per yearPayoff if there is a default by reference 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

7、析课程， George Yuan， 2013-14Other Details Payments are usually made quarterly in arrears In the event of default there is a final accrual payment by the buyer Settlement can be specified as delivery of the bonds or (more usually) in cash An auction process usually determines the payoff Suppose payments

8、 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 rate is 40%?金融工程案例分析课程， George Yuan， 2013-14Attractions of the CDS Market Allows credit risks to be traded in the same way as market risks Can be used to transfer

9、credit risks to a third party Can be used to diversify credit risks 金融工程案例分析课程， George Yuan， 2013-14Using a CDS to Hedge a Bond Position Portfolio 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 (app

10、roximately) a long position in a riskless instrument paying 5% per year This shows that bond yield spreads (measured relative to LIBOR) should be close to CDS spreads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-neut

11、ral) probability of default of 2% in each of the next 5 years. Assume payments are made annually in arrears, that defaults always happen half way through a year, and that the expected recovery rate is 40% Suppose that the breakeven CDS rate is s per dollar of notional principal金融工程案例分析课程， George Yua

12、n， 2013-14Unconditional Default and Survival Probabilities (Table 24.1)金融工程案例分析课程， George Yuan， 2013-14Calculation of PV of Payments(Table 24.2 Principal=$1)金融工程案例分析课程， George Yuan， 2013-1413Present Value of Expected Payoff (Table 24.3; Principal = $1)金融工程案例分析课程， George Yuan， 2013-14PV of Accrual Pa

13、yment Made in Event of a Default. (Table 24.4; Principal = $1)金融工程案例分析课程， George Yuan， 2013-14Putting it all together PV of expected payments is 4.0704s + 0.0426s = 4.1130s The breakeven CDS spread is given by4.1130s = 0.0511 or s = 0.0124 (124 bps) The value of a swap negotiated some time ago with

14、a CDS spread of 150bps would be 4.11300.01500.0511 = 0.0106per dollar of the principal.金融工程案例分析课程， George Yuan， 2013-14Implying Default Probabilities from CDS spreads Suppose that the mid market spread for a 5 year newly issued CDS is 100bps per year We can reverse engineer our calculations to concl

15、ude 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 throughout金融工程案例分析课程， George Yuan， 2013-14Binary CDS (page 554) T

16、he payoff in the event of default is a fixed cash amount In our example the PV of the expected payoff for a binary swap is 0.0852 and the breakeven binary CDS spread is 207 bps金融工程案例分析课程， George Yuan， 2013-14Credit Indices CDX NA IG is a portfolio of 125 investment grade companies in North America i

17、Traxx Europe is a portfolio of 125 European investment grade names The portfolios are updated on March 20 and Sept 20 each year The index can be thought of as the cost per name of buying protection against all 125 names金融工程案例分析课程， George Yuan， 2013-1419The Use of Fixed CouponsIncreasingly CDSs and C

18、DS 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 (CouponSpread)Duration is the amount the spread has to be

19、 multiplied by to get the PV of spread payments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 forward contract ceases to exist Example: Europea

20、n 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 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 reference entities are specified In a first to defa

21、ult swap there is a payoff when the first entity defaults Second, third, and nth to default deals are defined similarly Why does pricing depends on default correlation?金融工程案例分析课程， George Yuan， 2013-14Total Return Swap (page 558-559) Agreement to exchange total return on a portfolio of assets for LIB

22、OR plus a spread At the end there is a payment reflecting the change in value of the assets Usually used as financing tools by companies that want exposure to assets Total ReturnPayerTotal Return ReceiverTotal Return on AssetsLIBOR plus 25bps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

23、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1章: 信用互换衍生品（CDS）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3章: 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 Securities25What is Wrong? 金融工程案例分析课程， George Yuan， 2013-14251)The Pricing of C

24、DO 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 criterion used by S&P and Fitch does not satisfy the no-arbitrage condition.

25、(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 and bond yields as well as default correlation are the main concern. Unders

26、tanding 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 grade will itself be a major step forward in credit rating reform.WThe Credit

27、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 in the US relaxed their lending standards and created large numbers of

28、 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 further Features of the market: 100% mortgages, ARMs, teaser rates, NINJAs,

29、 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 the promised return was significantly higher than the cost of funds and

30、 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 options.U.S. real estate prices fell and products, created from the mortgag

31、es, 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) A “waterfall” defines the precise rules for allocating cash flows to tr

32、anchesAsset 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, George_Yuan 2013-2014ABSThe WaterfallEquity TrancheSenior TrancheMezzanine

33、 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%)AAAMezzanine Tranche (20%) BBBEquity Tranche (5%)How much of the original portfol

34、io of subprime mortgages is AAA?33Credit_VaR_Summary, George_Yuan 2013-2014 ABSs ABS CDOLosses to AAA Tranche of ABS CDO (Table 6.1)34Credit_VaR_Summary, George_Yuan 2013-2014A More Realistic Structure (Figure 6.5)Subprime MortgagesAAAAAABBBBB, NRSenior AAAJunior AAAAAABBBNRSenior AAAJunior AAAAAABB

35、BNRSenior 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 Tranches BBB tranches of ABSs were often quite thin (1% wide) This means that they have a quite different loss distribution

36、 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 Arbitrage Capital required for securities created from

37、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 Incentives Arguably the incentives of valuers, the creators of ABSs and ABS CDOs, and rating agencies helped to create

38、the crisis Compensation plans of traders created short-term horizons for decision making Credit_VaR_Summary, George_Yuan 2013-201438Importance of Transparency ABSs and ABS CDOs were complex inter-related products Once the AAA rated tranches were perceived as risky they became very difficult to trade

39、 because investors realized they did not understand the risks Other 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 exuberance Do not u

40、nderestimate default correlations in stressed markets Recovery rate depends on default rate Compensation structures did not create the right incentives If a deal seems too good to be true (eg, a AAA earning LIBOR plus 100 bp) it probably is Do not rely on ratings Transparency is important in financi

41、al markets Resecuritization 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， Ge

42、orge Yuan， 2013-1442 Cash CDO: 现金现金CDO Synthetic CDO: 合成合成 CDOAsset Backed Securities Securities created from a portfolio of loans, bonds, credit card receivables, mortgages, auto loans, aircraft leases, music royalties, etc Usually the income from the assets is tranched A “waterfall” defines how in

43、come 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，

44、从上到下。 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 tranchesPlus Systematic RiskNo

45、-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 no

46、t necessary correct : CRAs calculate EL in the real world (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 challe

47、nge problem.Duan and van Laere (2012) indicate that having 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 under

48、lying assets are debt obligations A synthetic CDO involves forming a similar structure with short CDS contracts In a synthetic CDO most junior tranche bears losses first. After it has been wiped out, the second most junior tranche bears losses, and so onAsset Backed Securities金融工程案例分析课程， George Yuan

49、， 2013-1448 Cash CDO: 现金现金CDO Synthetic CDO: 合成合成 CDO 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

50、 Yuan， 2013-1449金融工程案例分析课程， George Yuan， 2013-14Synthetic CDO Example金融工程案例分析课程， George Yuan， 2013-1451合成合成CDO Example金融工程案例分析课程， George Yuan， 2013-1452合成合成CDO Example金融工程案例分析课程， George Yuan， 2013-1453Synthetic CDO Details The income is paid on the remaining tranche principal. Example: when losses h

51、ave 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 principal金融工程案例分析课程， George Yuan， 2013-1454Single Tranche Trading This involves trading tranches of portfolios of CDSs without actually formin

52、g the portfolios Cash flows are calculated in the same way as they would be if the portfolios had been formed 金融工程案例分析课程， George Yuan， 2013-1455Quotes for Standard Tranches of iTraxx (Table 24.6)Quotes are 30/360 in basis points per year except for the 0-3% tranche where the quote equals the percent

53、 of the tranche principal that must be paid upfront in addition to 500 bps per year. 金融工程案例分析课程， George Yuan， 2013-1456 Example for CDX Index-Page 1Example CDX.NA.IG.20金融工程案例分析课程， George Yuan， 2013-1457 Example for CDX Index-Page 2Example CDX.NA.IG.20金融工程案例分析课程， George Yuan， 2013-1458 Example for CD

54、X Index-Page 3Example CDX.NA.IG.20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( (2014年年7日下午日下午2:30pm-5:00pm) 第1章: 信用互换衍生品（CDS）定价介绍第2章: 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）60合成合成-CDO Pricing, P.402金融工程案例分

55、析课程， George Yuan， 2013-1460Let S be the Spread on a given tranche each year CDO expected payment PV: S * A , A=Sigma, CDP Expected return is C , C=Sigma,Accrual Payment Amount (Before Loss happening) PV is S*B, B=Sigma, B=sigma,For the Buyer of Trunche (for Credit Risk Buyer), the Trunche PV is C- S

56、*A S*B,Thus the fair value should be C-S*A-S*B= 0, i.e.,C=S*A + S*B= S*(A+B)合成合成-CDO Pricing, P.402金融工程案例分析课程， George Yuan， 2013-1461CDO expected payment PV: S * A , A=Sigma, CDD Expected return is C , C=Sigma,Accrual Payment Amount (Before Loss happening) PV is S*B, B=Sigma金融工程案例分析课程， George Yuan，

57、2013-14Valuation of Tranches of Synthetic CDOs and Basket CDSs (page 562-566) A popular approach is to use a factor-based Gaussian copula model to define correlations between times to default Often all pairwise correlations and all the unconditional default distributions are assumed to be the same M

58、arket likes to imply a pairwise correlations from market quotes. 金融工程案例分析课程， George Yuan， 2013-14Cumulative Default Probability Conditional on FactorThe probability of k defaults from n names by time t conditional on F isThis enables cash flows conditional on F to be calculated. By integrating over

59、F the unconditional distributions are obtained1)()(1FtQNNFtQknkFtQFtQkknn1 )(!)!(!64Cumulative Default Probability Conditional on Factor金融工程案例分析课程， George Yuan， 2013-1464CDO Pricing(1)金融工程案例分析课程， George Yuan， 2013-1465CDO Pricing(1-More )金融工程案例分析课程， George Yuan， 2013-1466CDO Pricing (2)金融工程案例分析课程， George Yuan， 2013-1467CDO Pricing(3)金融工程案例分析课程， George Yuan， 2013-1468CDO Pricing(4a)金融工程案例分析课程， George Yuan， 2