Consider a four-year credit default swap on an underlying reference bond (with annual spread payments).

Suppose that the risk-free zero curve is flat at 3% per annum with continuous compounding.

The reference bond pays an annual coupon of 5% per year.

The probabilities of default during each of the next four years are 0.01, 0.015, 0.02, and 0.025, respectively.

(a) Assuming that the recovery rate is 20%, calculate the credit default swap spread.

(b) How much does the CDS spread change when the recovery rate becomes 40%?