Assignment:
In an annual-pay cap, the Black volatilities for caplets with maturities 1,2, 3, and 5 years are 18%, 20%, 22%, and 20%, respectively. Estimate the volatility of a one-year forward rate in the LIBOR market model when the time to maturity is (a) 0 to 1 year, (b) 1 to 2 years, (c) 2 to 3 years, and (d) 3 to 5 years. Assume that the zero curve is flat at 5% per annum (annually compounded). Use DerivaGem to estimate flat volatilities for 2-, 3-, 4-, 5-, and 6-year caps.