Question

A financial institution has entered into an interest rate swap with compony Y. Under the terms of the swap, it receives 8% per annum and pays 6-month LIBOR on a principal of $10 million for 5 years. Payments are made every 6 months. Suppose that company Y defaults on the sixth payment date (at the end of year 3) when the interest is 5% per annum for all maturities. What is the loss to the financial institution?

Answer 1

The loss suffered by the financial institution owing to company Y's default should equal the swap value at the end of Year 3 (swap value from the financial institution's perspective).

Swap Value from the Financial Institution's Perspective = PV of Fixed Interests Leg Cash Flows - PV of Floating LIBOR Leg Cash Flows

Remaining Swap Tenure = 2 years or 4 half-years, Fixed Coupon = 8 % per annum, Notional = $ 10 million and Applicable Interest Rate = 5 % per annum

Semi-Annual Fixed Leg Coupon = 0.08 x 10000000 x 0.5 = $ 400000

PV of Fixed Leg = 400000 x (1/0.025) x [1-{1/(1.025)^(4)}] + 10000000 / (1.025)^(4) = $ 10564296.13

PV of Floating Leg = Notional Value (as the floating leg's PV resets to the notional value at each coupon payment date) = $ 10000000

Therefore, Loss Suffered by Financial Institution = 10564296.13 - 10000000 = $ 564296.13