Suppose that the LIBOR yield curve is flat at 8% (with continuous compounding). The payoff from a derivative occurs in 4 years. It is equal to the 5-year rate minus the 2-year rate at this time, applied to a principal of $100 with both rates being continuously compounded. (The payoff can be positive or negative.)
Calculate the value of the derivative. Assume that the volatility for all rates is 25%.
What difference does it make if the payoff occurs in 5 years instead of 4 years? Assume all rates are perfectly correlated.