1.Under the terms of an interest rate swap, a financial institution has agreed to pay 10%...

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?

Solutions

Expert Solution

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

jeff jeffy answered 1 year ago

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