Use the DerivaGem software to value 1 x 4, 2 x 3, 3 x 2, and 4 x 1 European swap options to receive fixed and pay floating. Assume that the 1-, 2-, 3-, 4-, and 5-year interest rates are 6%, 5.5%, 6%, 6.5%, and 7%, respectively. The payment frequency on the swap is semiannual and the fixed rate is 6% per annum with semiannual compounding. Use the Hull-White model with a = 3% and a = 1%. Calculate the volatility implied by Black's model for each option.