1. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Credit Derivatives Chapter 23 1

2. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Credit Derivatives Derivatives where the payoff depends on the credit quality of a company or sovereign entity The market started to grow fast in the late 1990s 2

3. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Credit Default Swaps (page 501) 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 may be deliverable) 3

4. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 CDS Structure 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 4

5. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Other Details Suppose payments are made quarterly in the example just considered. What are the cash flows if there is a default after 3 years and recovery rate is 40%? 5

6. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 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 6

7. Credit Indices CDX NA IG tracks the average CDS spread for a portfolio of 125 investment grade (rated BBB or above) North American companies iTraxx Europe tracks the average CDS spread for a portfolio of 125 investment grade European companies Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 7

8. CDS Spreads and Bond Yields (See page 505) Portfolio consisting of a 5-year 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 CDS spreads should be approximately the same as bond yield spreads 8

9. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Valuation Suppose that conditional on no earlier default a reference entity has a (risk-neutral) 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 9

10. Unconditional Default and Survival Probabilities (Table 23.2) Note that 0.02*0.98 equals 0.0196, this is the probability that the company survives to the second year and then defaults in that year. The probability of surviving to the end of the second year is 0.98 *0.98 which is 0.9604 Futures Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 10 Time (years) Default Probability Survival Probability 10.02000.9800 20.01960.9604 30.01920.9412

11. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Calculation of PV of Payments Table 23.3 (Principal=$1, s is the size of the payment) Time (yrs) Survival Prob Expected Paymt Discount Factor PV of Exp Pmt 10.98000.9800s0.95120.9322s 20.96040.9604s0.90480.8690s 30.94120.9412s0.86070.8101s 40.92240.9224s0.81870.7552s 50.90390.9039s0.77880.7040s Total 4.0704s 11

12. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Present Value of Expected Payoff Table 23.4 (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 Total 0.0511 12

13. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 PV of Accrual Payment made in event of a Default. Table 23.5 (Principal=$1) TimeDefault Prob Expected Accr Pmt Disc Factor PV of Pmt 0.50.02000.0100s0.97530.0097s 1.50.01960.0098s0.92770.0091s 2.50.01920.0096s0.88250.0085s 3.50.01880.0094s0.83950.0079s 4.50.01840.0092s0.79850.0074s Total 0.0426s 13

14. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Putting it all together PV of expected payments is 4.0704s+0.0426s=4.1130s The breakeven CDS spread is given by 4.1130s = 0.0511 or s = 0.0124 (124 bps) 14

15. Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 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 probability is 1.61% per year. Note that is the CDS is fairly priced then it will be worth zero when it is signed. This would be true for a fairly priced option of any kind 15