A financial institution has entered into an interest rate sw

A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 10% per annum and pays six-month LIBOR on a principal of $10 million for five years. Payments are made every six months. Suppose that company X defaults on the sixth payment date (end of year 3) when the LIBOR/swap interest rate (with semiannual compounding) is 8% per annum for all maturities. What is the loss to the financial institution? Assume that six-month LIBOR was 9% per annum halfway through year 3. Use LIBOR discounting

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Solution

At the end of year 3 the financial institution was due to receive $500,000 (0.5*10% of $10million) and pay $450,000 (0.5*9% of $10 million).

The immediate loss is therefore $50,000. To value the remaining swap we assume than forward rates are realized. All forwardrl rates are 8% per annum.

The remaining cash flows are therefore valued on the assumption that the floating payment is 0.5*0.08*10000000=$400 000 and

the net payment that would be received is 500000-400000=$100000.

The total cost of default is therefore the cost of foregoing the following cash flows:

3 year: $50,000

3.5 year: $100,000

4 year: $100,000

4.5 year: $100,000

5 year:$100,000

Discounting these cash flows to year 3 at 4% per six months we obtain the cost of the default is $413000.

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