Use the DerivaGem software to value 1 × 4, 2 × 3, 3 × 2, and 4 × 1 European swap options to receive floating and pay fixed. Assume that the one, two, three, four, and five year interest rates are 3%, 3.5%, 3.8%, 4.0%, and 4.1%, respectively. The payment frequency on the swap is semiannual and the fixed rate is 4% per annum with semiannual compounding. Use the lognormal model with a = 5%, σ = 15%, and 50 time steps. Calculate the volatility implied by Black's model for each option.