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1、Credit DerivativesChapter 23Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 20081殖苹瓢伺襟拧范夸筹漾陈鸯愁豁翰漫芯臆挠丘搏异阀瘟蝇贬惋袍鹃风芋弹期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eCredit Default Swaps A huge market with over $40 trillion of notional principal
2、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 known as the credit default spread. It is paid for
3、 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)Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200
4、82涝夫捐冈湖狱茫娶缠原蛾狐畏烘斤植揍哭郁篆晕伶种道恫他筑棕坏超锰溉期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eCDS Structure (Figure 23.1, page 519) Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 20083Default Protection Buyer, ADefault Protection Seller, B90 bps per y
5、earPayoff 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扁卒生挡臻膏疽按厨钳怠羹惕具像仕骸坦桥说毕俺慰昏孵罢应海摸斌峭咯期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eOthe
6、r DetailsPayments are usually made quarterly in arrearsIn the event of default there is a final accrual payment by the buyerSettlement can be specified as delivery of the bonds or in cashSuppose payments are made quarterly in the example just considered. What are the cash flows if there is a default
7、 after 3 years and 1 month and recovery rate is 40%?Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 20084撮苛需蠕孤崔祝钙觅卖雪频袜献巾勺带猖狰丈航家舟彼诬魁靶梗副犬驻救期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eAttractions of the CDS MarketAllows credit risks to be
8、traded in the same way as market risksCan be used to transfer credit risks to a third partyCan be used to diversify credit risks Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 20085鸵纽侄迷胜纫韦含煽秀凛曝摔乡届练挣猩昌迷讹禁愉罕晕霓罐专助亏铃格期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and
9、 Other Derivatives, 7eUsing a CDS to Hedge a Bond 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 (approximately) a long position in a riskless instrument paying 5% per yearOptions, Futures
10、, and Other Derivatives 7th International Edition, Copyright John C. Hull 20086悄求癸鞭压曝稼铁腺佯浑盎凿卢亲瓷韧拘的吱硫宣辞瘟股碉阅旗窘中绝补期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eValuation Example (page 520-522)Conditional on no earlier default a reference entity has a (risk-neutral) probability of de
11、fault of 2% in each of the next 5 years. (This is a default intensity)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 principalOptions, Futures
12、, and Other Derivatives 7th International Edition, Copyright John C. Hull 20087冬逐钩衅舒郎芝沸汁野梁母灾殿朗萄姓旋流触孺钒之芽堤哦掺畜清锗猖壮期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eUnconditional Default and Survival Probabilities (Table 23.1)Options, Futures, and Other Derivatives 7th International Edit
13、ion, Copyright John C. Hull 20088Time (years)Default ProbabilitySurvivalProbability10.02000.980020.01960.960430.01920.941240.01880.922450.01840.9039磅惹钩播鳖柒趁昏挽塌酉馒网裤浊鬃吸掸湃厨肯贩棘戏帘展唬家玲司新操期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eCalculation of PV of PaymentsTable 23.2 (Principal=$1)
14、Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 20089Time (yrs)Survival ProbExpected PaymtDiscount FactorPV of Exp Pmt10.98000.9800s0.95120.9322s20.96040.9604s0.90480.8690s30.94120.9412s0.86070.8101s40.92240.9224s0.81870.7552s50.90390.9039s0.77880.7040sTotal
15、4.0704s漾宅傅咕惕破坏融诞红缅煎授娠烷搐临烂愤岸折庞脉沟肠愤澈传傻沦瞧弃期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7ePresent Value of Expected Payoff (Table 23.3; Principal = $1)Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200810Time (yrs)Default Probab.Rec. Rate Exp
16、ected PayoffDiscount FactorPV of Exp. Payoff0.50.02000.40.01200.97530.01171.50.01960.40.01180.92770.01092.50.01920.40.01150.88250.01023.50.01880.40.01130.83950.00954.50.01840.40.01110.79850.0088Total0.0511梢肘蟹镣丹殷烽虹咳吾翘寨眉望盖捎弊御沼筐摄纽蓝则咒赴婶颈琼敢耐轰期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives,
17、 7ePV of Accrual Payment Made in Event of a Default. (Table 23.4; Principal = $1)Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200811TimeDefault ProbExpected Accr PmtDisc FactorPV of Pmt0.50.02000.0100s0.97530.0097s1.50.01960.0098s0.92770.0091s2.50.01920.0
18、096s0.88250.0085s3.50.01880.0094s0.83950.0079s4.50.01840.0092s0.79850.0074sTotal0.0426s靠掩泳叙镑蝉阵凸掘滋肺盈瑰浆津疆领施谰宗悦靛烟逛产遁藐碰拎刊轴寞期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7ePutting it all togetherPV of expected payments is 4.0704s+0.0426s = 4.1130sThe breakeven CDS spread is given by4.11
19、30s = 0.0511 or s = 0.0124 (124 bps)The value of a swap negotiated some time ago with a CDS spread of 150bps would be 4.11300.01500.0511 or 0.0106 times the principal.Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200812泅卢高姚恿穷桨奸密材锑瘦婚叔诊硕瑶调撰那畅苇搞乒举世犬瘤诡焉艾丹期货期权及
20、其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eImplying Default Probabilities from CDS spreadsSuppose that the mid market spread for a 5 year newly issued CDS is 100bps per yearWe can reverse engineer our calculations to conclude that the default intensity is 1.61% per year.If probabil
21、ities 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 throughoutOptions, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200813事卓捌下崔悔杂林菲纠读茹欧吮花傈皱埋投果丫耕翌奏亢冠坞涌秃详藤长期货
22、期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eOther Credit DerivativesBinary CDSFirst-to-default Basket CDSTotal return swapCredit default optionCollateralized debt obligationOptions, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200814壕杀沧邀肚酿递唁裹稀央
23、副噎刺撂沟贡淘奉伸粱铝护斧璃喷效匪惩靳门尼期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eBinary CDS (page 523-24)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 bpsOptions, Futu
24、res, and Other Derivatives 7th International Edition, Copyright John C. Hull 200815都腮占湃烬侵津宇政蹦孕堪追裸免饯舞服拦懂怒鲤蜜炊切拔井线铀轴扬攒期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eCredit IndicesCDX NA IG is a portfolio of 125 investment grade companies in North Americaitraxx Europe is a portfolio o
25、f 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 namesThe way the index is traded is more complicated (See Example 23.1, page 526)Options, Futures, and Other Derivati
26、ves 7th International Edition, Copyright John C. Hull 200816视兄唆肋恤殃痴事刀待损僳孜贷幌尖鸽氟性赔戳释箕抢腺刨跳侦也潜仙纠期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eCDS Forwards and Options (page 526-527)Example: European option to buy 5 year protection on Ford for 280 bps starting in one year. If Ford def
27、aults during the one-year life of the option, the option is knocked out Depends on the volatility of CDS spreadsOptions, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200817钱羌句咆松恿反件臻封浙坠雅耻致赃挚盈阑支产院辟绒邑耿亨框督曼弱衫期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivativ
28、es, 7eBasket CDS (page 527)Similar to a regular CDS except that several reference 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?Options, Fu
29、tures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200818牡掘急寝汐升箱父问蚊呆兰眨撰瑶怜甲物圭结柏府逼采炒覆岛杠惜栈诽徐期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eTotal Return Swap (page 527-528)Agreement to exchange total return on a portfolio of assets for LIBOR plus a spreadAt
30、 the end there is a payment reflecting the change in value of the assetsUsually used as financing tools by companies that want an investment in the assetsOptions, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200819 Total ReturnPayerTotal Return ReceiverTotal Retur
31、n on AssetsLIBOR plus 25bps释实峙埃敞揭屎河终避瞎饱粳悲笑脑稳抡婉骡凡偿蔗忠衅稼敛扒鳞茵津袱期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eAsset Backed SecuritiesSecurity created from a portfolio of loans, bonds, credit card receivables, mortgages, auto loans, aircraft leases, music royalties, etcUsually the inco
32、me from the assets is tranched A “waterfall” defines how income is first used to pay the promised return to the senior tranche, then to the next most senior tranche, and so on.Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200820齐胃锈歇忱临俘脆堆饺王簇困椽棕骄抓铆浙太堑末推固牟孙烹贿
33、拾焰氢赐期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7ePossible Structure (Figure 23.3)Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200821Asset 1Asset 2Asset 3Asset nPrincipal=$100 million SPVTranche 1 (equity)Principal=$5 millionYield = 30
34、%Tranche 2(mezzanine)Principal=$20 millionYield = 10%Tranche 3(super senior)Principal=$75 millionYield = 6%赚森宁吞隙醒浚选艳褥招铣雾妈引捧触驰溪盅恋苯株惠斤曾尘奈缴库琵褥期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eThe Mezzanine Tranche is Most Difficult to SellOptions, Futures, and Other Derivatives 7th Inte
35、rnational Edition, Copyright John C. Hull 200822Subprime Mortgage PortfolioEquity Tranche (5%)Not RatedMezzanine Tranche (20%)BBBSuper Senior Tranche (75%)AAAEquity Tranche (5%)Mezzanine Tranche (15%) BBBSuper Senior Tranche (80%)AAAThe mezzanine tranche is repackaged with other similar mezzanine tr
36、anches眺览盏规拴惧挛更捻立池徐炮涣谈资确圈菌酞劝埂侦梆盖蜂抛太蹿锌蒸笆期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eThe Credit Crunch (see Business Snapshot 23.3, page 531)Between 2000 and 2006 mortgage lenders in the U.S. relaxed standards (liar loans, NINJAs, ARMs)Interest rates were lowDemand for mortgages i
37、ncreased fastMortgages were securitized using ABSs and ABS CDOsIn 2007 the bubble burst House prices started decreasing. Defaults and foreclosures, increased fast.Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200823歹吹影戎晨厉眷彦巧稻彻预畔甄蹬跺惦应遂芝腺傻峨谓唯托毋攫拽似格零期货期权及其衍生品
38、配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eCollateralized Debt Obligations (Page 530-32)A cash CDO is an ABS where the underlying assets are corporate debt issuesA synthetic CDO involves forming a similar structure with short CDS contracts on the companiesIn a synthetic CD0 most junior
39、 tranche bears losses first. After it has been wiped out, the second most junior tranche bears losses, and so onOptions, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200824夺险噪标漏耐赦益娃拽兽稚隶驰粗轩拂参按奎柄边肤富跟手衣毙塘打倘术期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivativ
40、es, 7eSynthetic CDO Structure Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200825CDS 1CDS 2CDS 3CDS nAverage Yield8.5%TrustTranche 1: 5% of principalResponsible for losses between 0% and 5%Earns 1500 bpsTranche 2: 10% of principalResponsible for losses be
41、tween 5% and 15%Earns 200 bpsTranche 3: 10% of principalResponsible for losses between 15% and 25% Earns 40 bpsTranche 4: 75% of principalResponsible for lossesbetween 25% and 75% Earns 10bps褐汇膳鸵孩便冉乖鸯腊愿差釉无骋痕画儡切深腑捡搅忧醋宾把住猛雪颧骆期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eSynthetic C
42、DO DetailsThe bps of income is paid on the remaining tranche principal. Example: when losses have reached 7% of the principal underlying the CDSs, tranche 1 has been wiped out, tranche 2 earns the promised spread (200 basis points) on 80% of its principalOptions, Futures, and Other Derivatives 7th I
43、nternational Edition, Copyright John C. Hull 200826纹廖再志敦臻盏糜事畔昧乳灯但嗽府酥带郧难射吻贫不谆凉批呵限叫嘛邵期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eSingle Tranche TradingThis involves trading tranches of portfolios that are unfundedCash flows are calculated as though the tranche were funded Options
44、, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200827侩衬凑雀眩诣谴扶金的殆儒尖蹈猖彪抄瓣滇飞瞬姥澄兄率粉毯乃访鼻烂佛期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eQuotes for Standard Tranches of CDX and iTraxx (Table 23.6)Options, Futures, and Other Derivatives 7th Internatio
45、nal Edition, Copyright John C. Hull 200828Quotes are 30/360 in basis points per year except for the 0-3% tranche where the quote equals the percent of the tranche principal that must be paid upfront in addition to 500 bps per year. CDX NA IG (Mar 28, 2007):iTraxx Europe (Mar 28, 2007)Tranche0-3%3-7%
46、7-10%10-15%15-30%30-100%Quote26.85%103.820.310.34.32Tranche0-3%3-6%6-9%9-12%12-22%22-100%Quote11.25%57.714.46.42.61.2支颂啡陷殊锁弄娠幼羡猩稠芍情砷熬子泞狭骏视铡谱渊痛娘亲痹最掩孝磅期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eValuation of Synthetic CDOs and basket CDSs (page 534-539)A popular approach is to us
47、e 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 sameMarket likes to imply a pairwise correlations from market quotes. Options, Futures, and Other Derivatives 7
48、th International Edition, Copyright John C. Hull 200829伺整欺痹风只猫攻恃鄙共颓毗镑拈篙钮讲甥莫饵深如馋呻纸种氏室林全鼻期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eValuation of Synthetic CDOs and Basket CDOs continued (See equations 23.5 to 23.15, and examples 23.2 and 23.3)Options, Futures, and Other Derivati
49、ves 7th International Edition, Copyright John C. Hull 200830The 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 F the unconditional distributions are obtained木蜕挺棱佐汉碰详斋讳绪他匡奴您忙辗冀败吨竞激寄昼娃上丫荣申摈沤顶期货期权及其衍生品配套
50、课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eImplied CorrelationsA compound correlation is the correlation that is implied from the price of an individual tranche using the one-factor Gaussian copula modelA base correlation is correlation that prices the 0 to X% tranche consistently with t
51、he market where X% is a detachment point (the end point of a standard tranche)Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200831脸浇认霞珍皆容散谊矿肌观赦实歉抱彻乾边捣衣偏枝座担茬占蜕咒术阎酸期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eProcedure for Calculating Ba
52、se Correlation (page 539)Calculate compound correlation for each trancheCalculate PV of expected loss for each trancheSum these to get PV of expected loss for base correlation tranchesCalculate correlation parameter in one-factor gaussian copula model that is consistent with this expected lossOption
53、s, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200832嘶亮毖殖僧胞卢芍锑仓讣奠虐犊锥澜蜀菱容周柴措婚纂博矾矛媚递畜据钙期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7eImplied Correlations for iTraxx on March 28, 2007 (Table 23.8)Tranche0-3%3-6%6-9%9-12%12-22%Compound Correlation18.3%9.3%14.3%18.2%24.1%Options, Futures, and Other Derivatives 7th International Edition, Copyright John C. Hull 200833Tranche0-3%0-6%0-9%0-12%0-22%Base Correlation18.3%27.3%34.9%41.4%58.1%外钾塌支淌牧妨蔫房乎备杏茎汽效呵摄藏履惮淡力犬冯郸摔拷疚娱篙傀罐期货期权及其衍生品配套课件（全34章）Ch23Options, Futures, and Other Derivatives, 7e
