Bonds maturing in 1,2,and 3 years have prices of 0.9323,0.8762,and 0.8002,respectively.A 0.8900 call on a 1-year bond matures in 1 year with σ = 0.25.What is the price of a 10.0% interest rate caplet that expires in 1 year?

Question

Quizplus · Accepted Answer

First, we need to calculate the forward rates for 1-2 years and 2-3 years:

Forward rate (1-2 years) = (0.8762/0.9323)^(1/1) -1 = -0.0601
Forward rate (2-3 years) = (0.8002/0.8762)^(1/1) -1 = -0.0869

Next, we can use the Black-76 model to price the caplet:

d1 = [ln(0.8900/0.9323) + (0.25^2)/2]/0.25 = -0.4446
d2 = -0.4446 - 0.25 = -0.6946

N(d1) = 0.3282
N(d2) = 0.2431

Price of caplet = 0.10 * (0.9323 * N(d1) - 0.8900 * N(d2)) = $0.70.

Therefore, the best choice is (C) $0.70.

Bonds Maturing in 1,2,and 3 Years Have Prices of 0