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2 October, 07:18

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 interest rate (with semiannual compounding) is 8% per annum for all maturities. What is the loss to the financial institution

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  1. 2 October, 07:32
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    The loss of the financial institution is $413,000

    Explanation:

    Let's say that after 3 years the financial institution will receive:

    0.5 * 10% of $10million

    = 0.5 * 0.1 * 10000000

    = $500,000

    Then, they will pay 0.5 * 9% of $10M

    = 0.5 * 0.09 * 10000000

    = $450,000

    Therefore, their immediate loss would be $500000 - $450000

    = $50000.

    Let's assume that forward rates are realized to value the rest of the swap.

    The forward rates = 8% per annum.

    Therefore, the remaining cash flows are assumed that floating payment is

    0.5*0.08*10000000 =

    $400,000

    Received net payment would be:

    500,000-400,000 = $100,000. The total cost of default is therefore the cost of foregoing the following cash flows:

    Year 3=$50,000

    Year 3.5=$100,000

    Year 4 = $100,000

    Year 4.5 = $100,000

    Year 5 = $100,000

    Discounting these cash flows to year 3 at 4% per six months, the cost of default would be $413,000
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