Question

1.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

Under the swap, the company can be considered to be having a long position in a floating-rate bond along with a short-position in a fixed rate bond.

For any floating rate payment, the immediate previous 3-month LIBOR is considered.

As soon as the next payment is made, the floating rate bond will be worth $100 million.

The next floating-rate payment can be calculated as => Notional amount * 3-month LIBOR one month ago * (Quarter of a year)

Hence, the next floating-rate payment = 100*0.118*0.25 = $2.95

The value of the floating-rate bond mentioned above is:

= $101.02288

where 0.115/4 is the quarterly applicable LIBOR and 2/12 is the time period ie. 2 months

The value of the fixed-rate bond ( by discounting the cash-flows at the applicable LIBOR =

The value of the fixed-rate bond = $98.9133

The value of the swap is, therefore, (Value of floating-rate bond - Value of fixed-rate bond) =$101.02288 - $98.9133 = $2.10958