The Current Market Conditions for an AAA Client Are 8

question 34

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.)

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Definitions:

Breach of Contract

The failure to perform as specified in a contract without a legitimate legal excuse.

Statute of Frauds

A legal concept that requires certain types of contracts to be executed in writing and signed by the party to be charged, in order to be enforceable.

Promissory Estoppel

Promissory estoppel is a legal doctrine that enforces a promise made when the promisee has relied on that promise to their detriment, even if a formal contract does not exist.

Good-Faith Reliance

Acting based on the honest belief or trust in the legitimacy or accuracy of something.