Question

An interest rate swap has 3 years of remaining life. Payments are exchanged annually. Interest at 3% is paid and 12-month LIBOR is received. A exchange of payments has just taken place. The 1 year, 2 years and three years LIBOR/swap zero rates are 2%, 3% and 4%. All rates an annually compounded. What is the value of the swap as a percentage of the principal when LIBOR discounting is used?

Answer 1

Answer:

2.66% of the principal.

Explanation:

Suppose the principal 100.

The value of the floating rate bond underlying the swap is 100.

The value of the fixed rate bond is 3/1.02 + 3/(1.03)^2 + 103/(1.04)^3 = 97.34.

The value of the swap is therefore 100−97.34 = 2.66 or 2.66% of the principal.

Answer 2

Answer: 2.66%

Explanation:

Let the principal be 100. Then the value of the floating rate bond underlying the swap is 100. The value of the fixed rate bond is 3/1.02+3/(1.03)2+103/(1.04)3=97.34. The value of the swap is therefore 100−97.34 = 2.66 or 2.66% of the principal.