The Current Market Conditions for an AAA Client Are 8

Essay

The current market conditions for an AAA client are 8% on a one-year dollar loan, and 8% fixed U.S. dollars for 9% fixed British pounds on a one-year dollar/pound currency swap. Let's consider a BBB client borrowing at (8 + m)% on a one-year dollar loan. The same client can enter a dollar/pound currency swap, paying (8 + µ)% fixed dollars and receiving 9% fixed pounds. Assume that the customer has a probability of p% to default within a year. In case of default, the bank knows that it will recover nothing on either transaction. The probability of default p (e.g., 5%) is known and independent of movements in interest and exchange rates. The spot exchange rate is S₀ = 1 $/£.
Assuming that you can observe the prices of $/£ currency options, suggest some approach to determine the fair values of m and µ. (Assume that the bank has a large number of clients whose probabilities of default are independent; therefore, the bank can diversify away the uncertainty of default on this specific client.)