Consider a one-year maturity caplet on underlying six-month Libor at a strike rate of 6%.If the forward rate is lognormal with volatility $\sigma = 0.10$ ,and the one-year spot rate is 5%,what is the price of a $100,000-notional caplet if the (1,1.5)-year forward rate is 6%?
A)$113.80
B)$139.34
C)$160.96
D)$227.59

Question

Quizplus · Accepted Answer

The caplet price can be calculated using the Black formula for caplets. Given the forward rate equals the strike rate, the caplet price is primarily determined by the volatility and the discount factor. The discount factor for one year at 5% is approximately 0.9512. Using the Black formula, the price is closest to $113.80.

Consider a One-Year Maturity Caplet on Underlying Six-Month Libor at a Strike