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Options, Futures, and Other Derivatives with Derivagem CD (7th Edition)

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Credit Derivatives Credit Derivatives Chapter 23 1 Options, Futures, and Other Derivatives 7th Edition, Copyright © John C. Hull 2008
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2008 2 Credit Default Swaps Credit Default Swaps A huge market with over $40 trillion of notional principal 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)
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2008 3 CDS Structure CDS Structure (Figure 23.1, page 527) (Figure 23.1, page 527) 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
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2008 4 Other Details 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%?
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2008 5 Attractions of the CDS Market 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
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2008 6 Using a CDS to Hedge a Bond 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
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2008 7 Valuation Example Valuation Example (page 528-530) (page 528-530) 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
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2008 8 Unconditional Default and Unconditional Default and Survival Probabilities Survival Probabilities (Table 23.1) (Table 23.1) Time (years) Default Probability Survival Probability 1 0.0200 0.9800 2 0.0196 0.9604 3 0.0192 0.9412 4 0.0188 0.9224 5 0.0184 0.9039
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Calculation of PV of Payments Calculation of PV of Payments Table 23.2 (Principal=$1) Table 23.2 (Principal=$1) Options, Futures, and Other Derivatives 7th Edition, Copyright © John C. Hull 2008 9 Time (yrs) Survival Prob Expected Paymt Discount Factor PV of Exp Pmt 1 0.9800 0.9800 s 0.9512 0.9322 s 2 0.9604 0.9604 s 0.9048 0.8690 s 3 0.9412 0.9412 s 0.8607 0.8101 s 4 0.9224 0.9224 s 0.8187 0.7552 s 5 0.9039 0.9039 s 0.7788 0.7040 s Total 4.0704 s
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