Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Credit Derivatives Chapter 23 Pages 501 – 515 ( middle) 1

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

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

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

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Other Details Payments are usually made quarterly or semiannually 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 a cash equivalent amount 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%? 5

Cheapest-to-deliver bond Usually there are a number of bonds that can be delivered in the event of a default The protection buyer can choose to deliver the bond with the lowest price In the case of cash settlement the calculation agent will base the calculation of the payoff on the cheapest-to-deliver bond Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull

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

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

CDS Spreads and Bond Yields (page 505) 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 CDS spreads should be approximately the same as bond yield spreads When is this likely not true? 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 10

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Unconditional Default and Survival Probabilities (Table 23.2) Time (years) Default Probability Survival Probability

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) Time (yrs) Survival Prob Expected Paymt Discount Factor PV of Exp Pmt s s s s s s s s s s Total s 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 Total

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 s s s s s s s s s s Total s 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 s s=4.1130s The breakeven CDS spread is given by s = or s = (124 bps) The value of a swap with a CDS spread of 150bps would be × or times the principal. 15

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Other Credit Derivatives Binary CDS Same as normal CDS but fixed $ payoff Not contingent upon a recovery rate Page 510 for example Total return swap Exchange total return on a bond for Libor plus a spread Total return includes coupons, interest, gain/loss on the asset during life of the swap Collateralized debt obligation 16

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Binary CDS (page 510) 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 and the breakeven binary CDS spread is 207 bps 17

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Total Return Swap (pages ) 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 18

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 CDS Options (page 513) 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 19

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Collateralized Debt Obligation (page 513) 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 earns a promised yield on remaining principal in the tranche 20

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Bond 1 Bond 2 Bond 3  Bond n Average Yield 8.5% Trust Tranche 4 Loss >25% Yield = 6% Tranche 3 Losses: 15-25% Yield = 7.5% Tranche 2 Losses: 5-15% Yield = 15% Tranche 1 Losses: 0-5% Yield = 35% Cash CDO Structure (Figure 23.3) 21

Fundamentals of Futures and Options Markets, 7th Ed, Ch 23, Copyright © John C. Hull 2010 Synthetic CDO Instead of buying the bonds the arranger of the CDO sells credit default swaps. Explain why this creates same “market” exposure What’s different about the “credit” exposure? 22

Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull Suggested Practice Problems