Question

Suppose that the risk-free zero curve is flat at $6 \%$ per annum with continuous compounding and that defaults can occur at times 0.25 years, 0.75 years, 1.25 years, and 1.75 years in a 2 -year plain vanilla credit default swap with semiannual payments. Suppose that the recovery rate is $20 \%$ and the unconditional probabilities of default (as seen at time zero) are $1 \%$ at times 0.25 years and 0.75 years, and $1.5 \%$ at times 1.25 years and 1.75 years. What is the credit default swap spread? What would the credit default spread be if the instrument were a binary credit default swap?

   Suppose that the risk-free zero curve is flat at $6 \%$ per annum with continuous compounding and that defaults can occur at times 0.25 years, 0.75 years, 1.25 years, and 1.75 years in a 2 -year plain vanilla credit default swap with semiannual payments. Suppose that the recovery rate is $20 \%$ and the unconditional probabilities of default (as seen at time zero) are $1 \%$ at times 0.25 years and 0.75 years, and $1.5 \%$ at times 1.25 years and 1.75 years. What is the credit default swap spread? What would the credit default spread be if the instrument were a binary credit default swap?

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 25, Problem 24

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Step 1

The expected default payments can be calculated by multiplying the unconditional probabilities of default by the notional amount and the recovery rate. Since the payments are semiannual, we need to discount them using the zero curve. For the first default at 0.25 Show more…

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Suppose that the risk-free zero curve is flat at $6 \%$ per annum with continuous compounding and that defaults can occur at times 0.25 years, 0.75 years, 1.25 years, and 1.75 years in a 2 -year plain vanilla credit default swap with semiannual payments. Suppose that the recovery rate is $20 \%$ and the unconditional probabilities of default (as seen at time zero) are $1 \%$ at times 0.25 years and 0.75 years, and $1.5 \%$ at times 1.25 years and 1.75 years. What is the credit default swap spread? What would the credit default spread be if the instrument were a binary credit default swap?

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