Question

Find the swap rate of a plain vanilla swap at initiation with 2 years to maturity, notional amount of $100 million, and semi-annual payments on both the fixed and floating legs. Assume the term structure is flat at 5% a year. Use semi-annual compounding.

Answer 1

Formula for swap rate as below in case of Plain Vanilla Swap

Swap rate = (1 - present value factor of cash flow at last payment date)/(summation of presnet value factor of cash flow of previous payment date)

Present value factor at 1st payment date = 1/(1 + .05/2)

= .9756

Present value factor at 2nd payment date = 1/(1 + .05/2)^2

= .9518

Present value factor at 3rd payment date = 1/(1 + .05/2)^3

= .9286

Present value factor at 4th payment date = 1/(1 + .05/2)^4

= .9060

Swap rate = (1 - .9060)/(.9756 + .9518 + .9286 + .9060)

= .025

= 2.5%

thus the swap rate for semiannual is 2.5% and annual rate will be 5%