Use the DerivaGems software to value 1x4, 2x3, 3x2, and 4x 1 European swap options to receive floating and pay food. Assume that the 1-, 2-, 3-, 3-, and 5-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%, 15%, and 50 time steps Calculate the volatility implied by Black's model for each option.