A firm is interested in purchasing an interest rate cap from a bank. It has received an offer price from the bank but would like to determine if the price is fair. The cap will consist of two caplets, one expiring in 91 days and the other in 182 days.
They will both have strikes of 7 percent. The forward rate applicable to the first caplet is 8 percent and the forward rate applicable to the second caplet is 8.2 percent. The 91- day risk-free rate is 7.1 percent and the 182-day risk-free rate is 7.3 percent.
All rates are continuously compounded. The firm's best estimate of the volatility of forward rates is 16.6 percent. The notional principal is $10 million, and the payoff is based on 90-day LIBOR. Use the Black model to determine a fair price for the cap.