Question: In an annual-pay cap the Black volatilities for at-the-money caplets which start in one, two, three, and five years and end one year later are

In an annual-pay cap the Black volatilities for at-the-money caplets which start in one, two, three, and five years and end one year later 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 the start of the period covered by the forward rate is (a) zero to one year, (b) one to two years, (c) two to three years, and (d) three to five years. Assume that the zero curve is flat at 5% per annum (annually compounded). Use DerivaGem with LIBOR discounting to estimate flat volatilities for two-, three-, four-, five-, and six-year at-the-money caps.

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