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 by equating the present value of the expected premium payments to the present value of the expected protection payments. Given a 5% probability of default each year and a 50% recovery rate, the expected loss given default is 50% of the notional amount. The expected premium payments need to compensate for this expected loss.For the first year, the expected loss is 5% (probability of default) * 50% (loss given default) = 2.5% of the notional. Since interest rates are zero, there's no discounting, so the expected premium payment for the first year compensates for this 2.5%.For the second year, there's a 95% chance (100% - 5% chance of default in the first year) that the contract is still active. The expected loss for the second year is then 95% * 5% (probability of default in the second year) * 50% (loss given default) = 2.375% of the notional.Adding these together, the total expected loss over the two years is 2.5% + 2.375% = 4.875% of the notional. To compensate for this expected loss over two years, the fair CDS spread is approximately 4.875% / 2 = 2.4375% or 243.75 bps. Since this option is not available, the closest available option is 250 bps.

Consider a Two-Year,annual Pay CDS Contract,where Premiums Are Paid at the End