Question

A two-year bond with a level annual coupon of 4.20 and a maturity value of 100 is priced at 101.291. The one-year spot rate is 0.045.

Based on this information what would be the swap rate for a two-year interest rate swap with level notional amount?

Answer 1

Let the two-year spot rate be R

Coupon Rate = 4.2 % and Maturity Value = $ 100, Actual Value = $ 101.291

Annual Coupon = 0.042 x 100 = $ 4.2

One-Year Spot Rate = 0.045 or 4.5 %

Therefore, 101.291 = 4.2 / (1+0.045) + [100 + 4.2] / [1+R]^(2)

97.27186 = (104.2) / (1+R)^(2)

R = [104.2/97.27186]^(1/2) - 1 = 0.035 or 3.5 %

Let the swap rate for a two year Interest Rate Swap be r

Therefore, 100 = r / (1.045) + (100 + r) / (1.035)^(2)

100 - 93.35107 = 1.890448r

r = 3.517119 % ~ 3.52 %