Consider a two-year, annual pay CDS contract, where premiums are paid at the end of the year and if default occurs, it is also assumed to happen at the end of the year (but immediately after the premium payment). Each year there is a 5% risk-neutral probability of the firm defaulting. In default, recovery is 50% (recovery of par, RP). Assume that interest rates are zero. The fair price of this CDS is a spread of
A) 200 bps
B) 225 bps
C) 250 bps
D) 275 bps

Question

Quizplus · Accepted Answer

The fair price of the CDS can be calculated considering the expected loss and the premium payments. Given a 5% default probability each year and a 50% recovery rate, the expected loss in case of default is 50% of the notional. Since default can occur at the end of the first or second year, we calculate the expected loss for each year and sum them up, considering the time value of money is zero (interest rates are zero).For the first year, the expected loss is 5% (probability of default) * 50% (loss given default) = 2.5% of the notional.For the second year, the default can only occur if it hasn't occurred in the first year. So, the probability of reaching the second year is 95% (100% - 5% probability of default in the first year), and then the probability of default in the second year is again 5%. Thus, the expected loss for the second year is 95% * 5% * 50% = 2.375% of the notional.The total expected loss over the two years is 2.5% + 2.375% = 4.875% of the notional.Since the CDS spread compensates for the expected loss and there are two premium payments (one at the end of each year), the fair CDS spread is the total expected loss divided by the number of payments, which is 4.875% / 2 = 2.4375%. This is approximately 243.75 bps, but since this option is not available, the closest available option is 250 bps.

Consider a Two-Year, Annual Pay CDS Contract, Where Premiums Are