Question

Assume corn forward prices over the next 3 years are 2.25, 2.35, and 2.28, respectively. Effective annual interest rates over the same period are 5.2%, 5.5%, and 5.8%. What is the 2-year swap price on a hypothetical ”forward swap” that begins at the end of year 1? (a) 2.14 (b) 2.32 (c) 2.41 (d) 2.53

Answer 1

Year (n)	1	2	3
Forward price (f)	2.25	2.35	2.28
Interest rate ('r)	5.20%	5.50%	5.80%

For the given forward prices, the present value of the cost for a 2-year forward swap is

f2/(1+r2)^2 + f3/(1+r3)^3 = 2.35/(1+5.50%)^2 + 2.28/(1+5.80%)^3 = 4.04

A swap will usually call for equal payment every year, so for a 2-year forward swap which begins at the end of year 2, the annual cost for this swap will be

c/(1+r2)^2 + c/(1+r3)^3 = 4.04

Solving for c,

c/(1+5.50%)^2 + c/(1+5.80%)^3 = 4.04

c/1.11 + c/1.18 = 4.04

(1.11+1.18)c = 4.04*1.18*1.11

c = (4.04*1.18*1.11)/(1.11+1.18) = 5.32/2.30 = 2.32 (option b)