Question

Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and receive three-month LIBOR in return on a notional principal of $100 million with payments being exchanged every three months. The swap has a remaining life of 11 months. Suppose the two-, five-, eight-, and eleven-month LIBORs are 11.5%, 11.75%, 12%, and 12.25%, respectively. The three-month LIBOR rate one month ago was 11.8% per annum. All rates are compounded quarterly. What is the value of the swap to the financial institution?

Answer 1

Solution:

The swap can be regarded as a long position in a floating-rate bond combined

with a short position in a fixed-rate bond.

Immediately after the next payment, the floating-rate bond will be worth $100

million. The next floating payment ($ million) is

$100 × 0.118 × 0.25 = $2.95

The value of the floating-rate bond is therefore = $102.95 ∗ (1 + 0.115/4)−4∗2/12

= $101.0229

The value of the fixed-rate bond is

-= $2.5(1 + 0.115/4)−4∗2/12 + $2.5(1 + 0.1175/4)−4∗5/12 + $2.5(1 + 0.12/4)−4∗8/12 + $102.5 ∗ (1 + 0.1225/4)−4∗11/12

= $98.9133

The value of the swap is therefore

$101.0229 − $98.9133 = $2.1096 million