Question

In an interest rate swap, ABC financial institution pays 6% per annum and receives three-month LIBOR in return on a notional principal of GBP 100 million with payments being exchanged every three months. The swap has a remaining life of 14 months. The average of the bid and offer fixed rates currently being swapped for three- month LIBOR is 8% per annum for all maturities. The three-month LIBOR rate one month ago was 7.8% per annum. All rates are compounded quarterly.
QUESTION: Calculate the value of the swap in terms of bonds

Answer 1

The Swap has 5 remaining payments.

1st payment after 2 months and then after 5,8,11 and 14 months

The Current 3 month LIBOR rate is equivalent to a fixed rate of 8% p.a. for all maturities i.e. the 3 month LIBOR rate for all the subsequent payment periods (other than the 1st payment) can be taken as 8% p.a.

The LIBOR rate for the 1st payment is 7.8%

The fixed rate bond pays GBP 100 million* 6%/4 = GBP1.5 million every period and discounted at 8%/4= 2% every 3 months

Value of fixed rate bond after 2 months = 1.5 + 1.5/1.02 + 1.5/1.02^2+1.5/1.02^3+101.5/1.02^4 =99.59614

Value of fixed rate bond today = 99.59614/1.02^(2/3) = 98.28993 million GBP

The floating rate payment after 2 months = GBP 100 million * 7.8%/4 = GBP 1.95 million

So, floating bond can be valued as if it is paying GBP 101.95 million in 2 months

So, Value of floating rate bond = 101.95/1.02^(2/3) = GBP 100.61293 million

So, Value of Swap to ABC which is a fixed rate payer = Value of floating bond - value of fixed bond

=100.61293 - 98.28993

= GBP 2.322993 million

or GBP 2,322,993