Question

A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, the six-month LIBOR is exchanged semi-annually for 12% per annum. The six-month LIBOR rate in swaps of all maturities is currently 10% per annum with continuous compounding. The six-month LIBOR rate was 9.6% per annum two months ago. What is the current value of the swap to the party paying floating? What is it's value to the party paying fixed?

Answer 1

Step-by-step explanation:

Fixed = 12% (exchanged for = receive)

Floating = LIBOR = 9.6% two months ago

Remaining life of swap = 10 months

6 month LIBOR rate for all maturities = 10% (used for discounting)

Receive:

Fixed = [(100)(0.12)(6/12) * e - 0.10 * (4/12)] + 106e - 0.10 * (10/12)= $103,328,005

Pay:

Floating = {100 + [(100)(.096)(.5)]} * e - .10 * (4/12)= $101,364,247

Value of swap to party paying floating: $103,328,004.6 - $101,364,247.3 = $1,963,757

Value of swap to party paying fixed =

- $1,963,757