Question

A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 4% 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 six-month forward LIBOR rates for all maturities are 2% per annum. What is the loss to the financial institution? Assume that six-month LIBOR was 3% per annum halfway through year 3 and that at the time of default all OIS rates are 1.8% per annum. OIS rates are expressed with continuous compounding; other rates are expressed with semiannual compounding

Answer 1

Sol :

A financial institution has entered into an interest rate swap with company X.

Under the terms of the swap, it receives 4% per annum and pays six-month LIBOR on a principal of $10 million for five years.

Company X defaults on the sixth payment date (end of year 3) when the six-month forward LIBOR rates for all maturities are 2% per annum.

Loss to the financial institution will be as follows,

At the end of 3 years the financial institution was due to received 0.5x4% of $10 million = $200,000

Payment woud be 0.5x3% of $10 million = $150,000

Therefore loss to the financial institution will be $200,000 - $150,000 = $50,000

Now assume the LIBOR forward rates are realised for valuing the remaining swaps.

Forward LIBOR rates for all maturities are 2% per annum.

Remaining cash flows will be valued on th basis of the assumption that the floating payment will be 0.5x2%x$10 million = $100,000.

Fixed payment = $200,000

Net payment to be received will be $200,000 - $100,000 = $100,000

Total cost of default will be foregoing the following cash flows - 3 year - $50,000, 3.5 years - $100,000, 4 years - $100,000, 4.5 years - $100,000, 5 years - $100,000.

After discounting these cash flows to 3rd year at 1.8% PA, cost of default will be $441,120