1. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.1 Credit Derivatives Chapter 21

2. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.2 Credit Derivatives Derivatives where the payoff depends on the credit quality of a company or country The market started to grow fast in the late 1990s By 2009 notional principal totaled $32 trillion

3. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.3 Credit 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 X Premium is known as the credit default spread. It is paid for life of contract or until default If 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)

4. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.4 CDS Structure (Figure 21.1, page 508) Default Protection Buyer, A Default Protection Seller, B 90 bps per year Payoff 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

5. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.5 Other 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 in cash Suppose 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%?

6. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.6 Attractions of the CDS Market Allows credit risks to be traded in the same way as market risks Can be used to transfer credit risks to a third party Can be used to diversify credit risks

7. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.7 Using 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 year This shows that bond yield spreads (measured relative to LIBOR) should be close to CDS spreads

8. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.8 Valuation Example (page 510-512) Conditional on no earlier default a reference entity has a (risk-neutral) probability of default 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 principal

9. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.9 Unconditional Default and Survival Probabilities (Table 21.1) Time (years) Default Probability Survival Probability 10.02000.9800 20.01960.9604 30.01920.9412 40.01880.9224 50.01840.9039

10. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.10 Calculation of PV of Payments Table 21.2 (Principal=$1) Time (yrs)Survival Prob Expected Paymt Discount Factor PV of Exp Pmt 10.98000.9800 s 0.95120.9322 s 20.96040.9604 s 0.90480.8690 s 30.94120.9412 s 0.86070.8101 s 40.92240.9224 s 0.81870.7552 s 50.90390.9039 s 0.77880.7040 s Total4.0704 s

11. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.11 Present Value of Expected Payoff ( Table 21.3; Principal = $1) Time (yrs) Default Probab. Rec. Rate Expected Payoff Discount Factor PV of Exp. Payoff 0.50.02000.40.01200.97530.0117 1.50.01960.40.01180.92770.0109 2.50.01920.40.01150.88250.0102 3.50.01880.40.01130.83950.0095 4.50.01840.40.01110.79850.0088 Total0.0511

12. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.12 PV of Accrual Payment Made in Event of a Default. ( Table 21.4; Principal=$1) TimeDefault Prob Expected Accr Pmt Disc Factor PV of Pmt 0.50.02000.0100 s 0.97530.0097 s 1.50.01960.0098 s 0.92770.0091 s 2.50.01920.0096 s 0.88250.0085 s 3.50.01880.0094 s 0.83950.0079 s 4.50.01840.0092 s 0.79850.0074 s Total0.0426 s

13. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.13 Putting it all together PV of expected payments is 4.0704 s +0.0426 s =4.1130 s The breakeven CDS spread is given by 4.1130 s = 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 4.1130×0.0150-0.0511 or 0.0106 times the principal.

14. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.14 Implying 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 conclude that the default intensity 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

15. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.15 Other Credit Derivatives Binary CDS First-to-default Basket CDS Total return swap Credit default option Collateralized debt obligation

16. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.16 Binary CDS (page 513) The 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

17. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.17 CDS Forwards and Options (page 514- 515) 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: European option to buy 5 year protection on Ford for 280 bps starting in one year. If Ford defaults during the one-year life of the option, the option is knocked out Depends on the volatility of CDS spreads

18. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.18 Total Return Swap (page 515-516) Agreement to exchange total return on a corporate bond for LIBOR plus a spread At the end there is a payment reflecting the change in value of the bond Usually used as financing tools by companies that want an investment in the corporate bond Total Return Payer Total Return Receiver Total Return on Bond LIBOR plus 25bps

19. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.19 First to Default Basket CDS (page 516) Similar to a regular CDS except that several reference entities are specified and there is a payoff when the first one defaults This depends on “default correlation” Second, third, and n th to default deals are defined similarly

20. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.20 Collateralized Debt Obligation (Figure 21.3, page 517) A pool of debt issues are put into a special purpose trust Trust issues claims against the debt in a number of tranches First tranche covers x % of notional and absorbs first x % of default losses Second tranche covers y % of notional and absorbs next y % of default losses etc A tranche earn a promised yield on remaining principal in the tranche

21. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.21 Bond 1 Bond 2 Bond 3  Bond n Average Yield 8.5% Trust Tranche 1 1 st 5% of loss Yield = 35% Tranche 2 2 nd 10% of loss Yield = 15% Tranche 3 3 rd 10% of loss Yield = 7.5% Tranche 4 Residual loss Yield = 6% CDO Structure

22. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.22 Synthetic CDO with examples Instead of buying the bonds the arranger of the CDO sells credit default swaps. Examples: Equity tranche is responsible for losses on underlying CDSs until they reach 5% of total notional principal (earns 1000 bp spread) Mezzanine tranche is responsible for losses between 5% and 20% (earns 200 bp spread) Senior tranche is responsible for losses over 20% (earns 10 bp spread)

23. Synthetic CDS details The income is paid on the remaining tranche 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 principal Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.23

24. Asset Backed Securities (ABS) 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 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 6 th Edition, Copyright © John C. Hull 2005 21.24

25. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull 2005 21.25