Credit Derivatives

Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Credit DerivativesChapter 231Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Credit DerivativesDerivatives where the payoff depends on the credit quality of a company or sovereign entityThe market started to grow fast in the late 1990s

2Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Credit Default Swaps (page 504-507)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 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 may be deliverable)3Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013CDS Structure 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 bond4Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Other 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 (more usually) a cash equivalent amountSuppose 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 rate is 40%?

5Attractions 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 Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 20136Moodys Statistics on Recovery Rates (1982-2011) Table 23.1 page 507Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013ClassAverage recovery rate (%)Senior secured51.5Senior unsecured36.8Senior subordinated30.9Subordinated31.5Junior subordinated24.777CDSs and BondsA 5-year bond plus a 5-year CDS produces a portfolio that is (approximately) risk-freeThis shows that bond yield spreads should be close to CDS spreadsThe CDS-bond basis is the excess of CDS spreads over the corresponding bond yield spreads. (Negative during the credit crisis)Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 20138The PayoffUsually there are a number of bonds that can be delivered in the event of a defaultThe protection buyer can choose to deliver the bond with the lowest priceIn practice an auction process is usually used to determine a cash payoffFundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 201399Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Attractions 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 10Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013CDS Spreads and Bond Yields (See page 506-507)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 yearThis shows that CDS spreads should be approximately the same as bond yield spreads 11Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013ValuationSuppose that conditional on no earlier default a reference entity has a (risk-neutral) probability of default of 2% in each of the next 5 yearsAssume 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

12Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Unconditional Default and Survival Probabilities (Table 23.2, page 508)Time (years)Default ProbabilitySurvivalProbability10.02000.980020.01960.960430.01920.941240.01880.922450.01840.903913Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Calculation of PV of PaymentsTable 23.3, page 509 (Principal=$1)Time (yrs)Survival ProbExpected PaymtDiscount FactorPV of Exp Pmt10.98000.9800s0.95120.9322s20.96040.9604s0.90480.8690s30.94120.9412s0.86070.8101s40.92240.9224s0.81870.7552s50.90390.9039s0.77880.7040sTotal4.0704s14Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Present Value of Expected Payoff Table 23.4, page 509 (Principal = $1)Time (yrs)Default Probab.Rec. Rate Expected PayoffDiscount FactorPV of Exp. Payoff0.50.02000.40.01200.97530.01171.50.01960.40.01180.92770.01092.50.01920.40.01150.88250.01023.50.01880.40.01130.83950.00954.50.01840.40.01110.79850.0088Total0.051115Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013PV of Accrual Payment made in event of a Default. Table 23.5, page 510 (Principal=$1)TimeDefault ProbExpected Accr PmtDisc FactorPV of Pmt0.50.02000.0100s0.97530.0097s1.50.01960.0098s0.92770.0091s2.50.01920.0096s0.88250.0085s3.50.01880.0094s0.83950.0079s4.50.01840.0092s0.79850.0074sTotal0.0426s16Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Putting 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 bp)The value of a swap with a CDS spread of 150bp would be 4.11300.0150 0.0511 or 0.0106 times the principal.

17Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Implying Default Probabilities from CDS SpreadsSuppose that the mid market spread for a 5 year newly issued CDS is 100bp per yearWe 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 throughout18Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Other Credit DerivativesBinary CDSFirst-to-default Basket CDSTotal return swapCredit default optionCollateralized debt obligation19Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Binary CDS (page 511-512)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 bps20Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013First to Default Basket CDS (page 512)Similar to a regular CDS except that several reference entities are specified and there is a payoff when the first one defaultsThis depends on default correlationSecond, third, and nth to default deals are defined similarly21Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Total Return Swap (pages 512-514)Agreement to exchange total return on a corporate bond for LIBOR plus a spreadAt the end there is a payment reflecting the change in value of the bondUsually used as financing tools by companies that want an investment in the corporate bond Total ReturnPayerTotal Return ReceiverTotal Return on BondLIBOR plus 25bps22CDS Forwards and Options (page 514)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 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 Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 201323Credit IndicesCDX NA IG tracks the average CDS sppread for a portfolio of 125 investment grade (rated BBB or above) North American companiesiTraxx Europe tracks the average CDS sppread for a portfolio of 125 investment grade European companies

Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 20132424The 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 (CouponSpread)Duration is the amount the spread has to be multiplied by to get the PV of spread payments. (In our example, it was 4.1130.)

Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 20132525Asset Backed Securities (ABSs)Securities 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 income is first used to pay the promised return to the senior tranche, then to the next most senior tranche, and so on.Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 20132626Collateralized Debt Obligations (Page 516-519)A cash CDO is an ABS where the underlying assets are debt obligationsA synthetic CDO involves 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 onFundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 201327Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Short CDS 1Short CDS 2Short CDS 3

Short CDS n

Total Principal=$100 million

Average spread= 100bpSPVTranche 1$75 millionSpread = 8bpTranche 2$10 millionSpread = 40bpTranche 3$10 millionSpread = 300bp Tranche 4$5 millionSpread = 800bpSynthetic CDO Structure (Figure 23.3)

28Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Standard Tranches Are Created from Standard PortfoliosCDX NA IG:Tranches: 0-3%, 3-7%, 7-10%, 10-15%, 15-30%, 30-100%iTraxx Europe:Tranches: 0-3%, 3-6%, 6-9%, 9-12%, 12-22%, 22-100%29Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013Single Tranche TradingWhere one tranche is traded without the other tranches being createdThe synthetic CDO structure is used as a reference for defining the cash flows (but it is never actually created)30Mid-Market Quotes for iTraxx Europe (Table 23.7, page 518)Tranche0-3%3-6%6-9%9-12%12-22%IndexJan 31, 200710.34%41.5911.955.602.0023Jan 31, 200830.98%316.90212.40140.0073.6077Jan 31, 200964.28%1185.63606.69315.6397.13165Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 20133131