Question

In an interest rate swap, a financial institution has agreed to pay 3.6% per annum and to 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 14 months. Three-month forward LIBOR for all maturities is currently 4% per annum. The three-month LIBOR rate one month ago was 3.2% per annum. OIS rates for all maturities are currently 3.8% with continuous compounding. All other rates are com-pounded quarterly. What is the value of the swap?

Answer 1

Notional	100	million
Pay Fixed	3.60%	per annum
Receive Variable	3 month libor
Exchange	every 3 months
Swap remaining life	14 months
3 month libor (last)	3.20%	per annum
Libor rate for all maturities	3.80%	per annum
The value of ' Pay Fix Receive Floating' swap can be expressed as
V = B (Float) - B(Fix)
Last libor maturity	2 months	60	days
Swap remaining life	14 months	420	days
B (Float)
=		Formula
0.2822	million	(3.2/100*60/360*100+1)/(1+3.8/100*420/360*100)
B(Fix)
=		Formula
0.3077	million	(3.6/100*60/360*100+1)/(1+3.6/100*420/360*100)
Thus value of Swap
=
V = B (Float) - B(Fix)
(0.0255)	million