Suppose that the 1-, 2-, 3-, 4-, and 5-year interest rates are 4%, 4.8%, 5.3%, 5.5%, and 5.6%, respectively. The volatility of all swap rates are 20%. A bank has entered into an annual-pay swap with a counterparty where the fixed rate exchanged for floating is 5.705%. The notional principal is $100 million. The spreads over the risk-free rates for 1 -, 2-, 3-, 4-, and 5-year bonds issued by the counterparty are 20, 40, 55, 65, and 75 basis points, respectively. Assume that defaults can occur only on payment dates and ignore any losses arising from payments that are due to be exchanged on the date of default. Use the DerivaGem software to answer the following questions:

a. What is the expected loss from defaults on a 5-year swap where the bank receives fixed?

b. What is the expected loss from defaults on a 5-year swap where the bank receives floating?

Explain why your answer here is higher than your answer to part (a).

c. What is the spread required by the bank on a matched pair of interest rate swaps to compensate for credit risk?

d. What difficulties are there in modifying your analysis to allow for losses arising from payments due to be made on the day of default?