Risk Management and Financial Institutions, + Web Site, 3rd Edition

APPENDIX K

Valuation of Credit Default Swaps

Credit default swaps (CDSs) are described in Chapter . They can be valued using (risk-neutral) default probability estimates.

Suppose that the probability of a reference entity defaulting during a year conditional on no earlier default is 2%. Table K.1 shows survival probabilities and unconditional default probabilities (that is, default probabilities as seen at time zero) for each of the five years. The probability of a default during the first year is 0.02 and the probability the reference entity will survive until the end of the first year is 0.98. The probability of a default during the second year is 0.02 × 0.98 = 0.0196 and the probability of survival until the end of the second year is 0.98 × 0.98 = 0.9604. The probability of default during the third year is 0.02 × 0.9604 = 0.0192 and so on.

We will assume that defaults always happen halfway through a year and that payments on a five-year credit default swap are made once a year, at the end of each year. We also assume that the risk-free interest rate is 5% per annum with continuous compounding and the recovery rate is 40%. There are three parts to the calculation. These are shown in Tables K.2, K.3, and K.4.

Table K.2 shows the calculation of the present value of the expected payments made on the CDS assuming that payments are made at the rate of s per year and the notional principal is $1. For example, there is a 0.9412 probability that the third payment of s is made. The expected ...