Question

Let's suppose that oil forward prices for 1 year, 2 years, and 3 years are $40, $41, and $42. The 1-year, 2-year, and 3-year effective annual interest rates are 2.0%, 2.5%, and 3.0%, respectively.

(a) What is the 3-year swap price?

(b) What is the price of a 2-year swap beginning in 1 year? (That is, the first swap settlement will be in 2 years and the second in 3 years.)

Answer 1

a) We first have to find present value of cost of three barrels based on forward prices

=40/(1.02) + 41/(1.025)^2 + 42/(1.03)^3 = $116.676

After this, we solve for the price x such that x such that x/(1.02) + x/(1.025)^2 + x/(1.03)^3 = 116.676:

=116.676/(1/(1.02) + 1/(1.025)^2 + 1/(1.03)^3) = $40.977

So swap price is $40.977

b) we will first find the present value of cost of two barres in year2 and year 3

=41/(1.025)^2 + 42/(1.03)^3 = $77.460

After this, we can obtain swap price by solving this equation : x/(1.025)^2 + x/(1.03)^3 = 77.460:

=77.460/(1/(1.025)^2 + 1/(1.03)^3) = $41.490