Question

6. Two parties enter into a 2-year fixed-for-floating interest rate swap with semiannual payment. The floating rate payments are based on LIBOR as follows. Find swap fixed rate.

Maturity (days)	Annualized rate	Discount factor, Z
180	0.05	0.9756
360	0.06	0.9434
540	0.065	0.9112
720	0.07	0.8772

After 180 days, the LIBOR rates and discount factors are as follows:

Maturity (days)	Annualized rate	Z
180	0.045	0.9780
360	0.050	0.9524
540	0.060	0.9174

What is the market value of the swap to the fixed rate payer if the notional principal is $1 million?

Answer 1

Swap rate at the initiation (t(0)) = (1-d(720))/(d(180)+d(360)+d(520)+d(720))

Swap rate at the initiation = (1-0.8772)/(0.9756+0.9434+0.9112+0.8772)

Swap rate at initiation = 0.0331 =3.31%

Swap fixed rate = 3.31%

Swap rate after 180 days = (1-d(540))/(d(180)+d(360)+d(540))

Swap rate after 180 days = 0.0290 = 2.90%

Market value of the swap to the fixed rate payer = ((0.045-0.0331 )*0.9780) + ((0.050-0.0331 )*0.9524) + ((0.060-0.0331 )*0.9174) * $1 million

Market value of the swap to the fixed rate payer = $52411.82