Topic 10_Fin80018

Topic 10Credit DerivativesEssential Reading:Hull (2014) Ch. 23*FIN80018 Derivatives and Risk ManagementAdapted from Hull (2014) Ch. 23

Fundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013

Credit DerivativesDerivatives where the payoff depends on the credit quality of a company or sovereign entityThe market started to grow fast in the late 1990s

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Credit 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)*


CDS 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 bond*


Other Details of CDSsPayments 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%?

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Attractions 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 *


CDSs 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)*


The 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 payoff*


Attractions 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 *


CDS 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 *


ValuationSuppose 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

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Calculate the probability of default survivalPV of SurvivalPV of defaultPV payoffAT break even]PV of survival + PV of default= PV of payoff*


Excel for PracticeFundamentals of Futures and Options Markets, 8th Ed, Ch 23, Copyright John C. Hull 2013*


Unconditional Default and Survival Probabilities default prob 2%(Table 23.2, page 508)*

Time (years)Default ProbabilitySurvivalProbability10.02000.98002(0.98*2) 0.01960.9604 (1-0.196)30.01920.941240.01880.922450.01840.9039


Calculation of PV of Payments s is expected payment for one dollar of principleTable 23.3, page 509 (Principal=$1)*

Time (yrs)Survival ProbExpected PaymtDiscount FactorPV of Exp Pmt10.98000.9800s0.95120.9322s20.96040.9604s0.90480.8690s30.94120.9412s0.86070.8101s40.92240.9224s0.81870.7552s50.90390.9039s0.77880.7040sTotal4.0704s


Present Value of Expected Payoff Table 23.4, page 509 (Principal = $1)*

Time (yrs)Default Probab.Rec. Rate Expected PayoffDiscount FactorPV of Exp. Payoff0.50.02000.40.01200.97530.01171.50.01960.40.01180.92770.01092.50.01920.40.01150.88250.01023.50.01880.40.01130.83950.00954.50.01840.40.01110.79850.0088Total0.0511


PV of Accrual Payment made in event of a Default. Table 23.5, page 510 (Principal=$1)*

TimeDefault ProbExpected Accr PmtDisc FactorPV of Pmt0.50.02000.0100s0.97530.0097s1.50.01960.0098s0.92770.0091s2.50.01920.0096s0.88250.0085s3.50.01880.0094s0.83950.0079s4.50.01840.0092s0.79850.0074sTotal0.0426s


Putting 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.

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Other Credit DerivativesBinary CDSFirst-to-default Basket CDSTotal return swapCredit default optionCollateralized debt obligation*


First 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 similarly*


Credit IndicesCDX NA IG tracks the average CDS spread for a portfolio of 125 investment grade (rated BBB or above) North American companiesiTraxx Europe tracks the average CDS spread for a portfolio of 125 investment grade European companies

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Asset 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.*


Collateralized 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 on*


Short 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)

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*Value of the contract today at spotValue is always 0 when buyingIf the basis or spread is 100 value is 0, above 100 positive number * principal and vice versaAny group to default first One in a group default triggers a payment in other groups in the basketDefault Correlation: Perfectly correlated means if one default all of them will default THEORY QUESTION*1 million / Mortgage Back Securities- all the mortgages added up---- Special Purpose Vehicle---- ABS---- Sell to investorsNow investros has ABS and the bank had raised 1 millionSynthertic CDO is the derivative of CDS, CDS is the derivative of ABS*

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Topic 10_Fin80018