Suppose that zero rates are as in Problem 21.14. Use DerivaGem (with LIBOR discounting) to determine the value of an option to pay a fixed rate of 6% and receive LIBOR on a five-year swap starting in one year. Assume that the principal is $100 million, payments are exchanged semiannually, and the swap rate volatility is 21%.

Problem 21.14

Suppose that the 1-year, 2-year, 3-year, 4-year and 5-year LIBOR/swap zero rates are 6%, 6.4%, 6.7%, 6.9%, and 7%. The price of a 5-year semiannual cap with a principal of $100 at a cap rate of 8% is $3. Use DerivaGem (with LIBOR discounting) to determine:

(a) The 5-year flat volatility for caps and floors

(b) The floor rate in a zero-cost 5-year collar when the cap rate is 8%.