Question

Suppose that the risk-free zero curve is flat at 7% per annum with continuous com pounding and that defaults can occur halfway through each year in a new 2-year credit default swap. suppose that the recovery rate is 30% and the default probabilities each year conditional on no earlier default is 3%. (a) estimate the credit default swap spread. assume payments are made annually. (b) what is the value of the swap per dollar of notional principal to the protection buyer if the credit default swap spread is 150 basis points? (c) what is the credit default swap spread if it is a binary cds? (d) verify that, if the cds spread is 100 basis points, the probability of default in a year (conditional on no earlier default) must be 1.3703%

Answer 1

The CDS spread compensates for credit risk above a risk-free rate and is estimated using default probabilities and recovery rates. The value to the protection buyer and the implied default probability are derived from the present value of expected payment streams.

To estimate the credit default swap (CDS) spread, take into account that the risk-free zero curve is flat at 7% per annum with continuous compounding. With a recovery rate of 30% and the default probabilities each year conditional on no earlier default at 3%, the estimated CDS spread would compensate for the credit risk above the risk-free rate. The valuation of the CDS from the protection buyer's standpoint with a CDS spread of 150 basis points involves discounting the expected loss and premium payments.

For a binary CDS, where the payoff is all or nothing, the credit spread would be adjusted to reflect this different structure. If the spread were 100 basis points, then by equating the expected loss to the premium, we could back out the implied probability of default.

To determine the value of the swap to the protection buyer and the implied default probability, the present value of payment streams is calculated considering default probabilities, recovery rates, and the given CDS spread.