Use the DerivaGem software to value $1 \times 4,2 \times 3,3 \times 2$, and $4 \times 1$ 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 $\sigma=1 \%$. Calculate the volatility implied by Black's model for each option.