Question

Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive six-month LIBOR in return on a notional principal of $100 million with payments being exchanged every 6 months. The swap has a remaining life of 4 months. The average of the bid and offer fixed rates currently being swapped for 6-month LIBOR is 12% per annum for all maturities. The 6-month LIBOR rate two months ago was 11% per annum. All rates are compounded semiannually. What is the value of the swap?

Answer 1

Swap valuation is based on the net benefit derived from the two cash flows streams i.e. fixed payouts vs floating payouts.

Hence to value the swap we calculate the difference between payouts at end of the 6 months period = Floating payout - Fixedpayout = [10 million x (1.11^0.5-1)] (floating) - $5,000,000(fixed) = $5,356,500 - $5,000,000 = $356,500

As this is the net difference between payouts at the end of 6months (which is four months away) we find the present value ofthis amount to arrive at the value of the swap

Value of Swap = PV of 356,500 = 356,500 / (1+(5.83%*4/6)) =$343,162