What does the calibration of a one-factor term structure model involve?
Use the DerivaGem software to value 1 × 4, 2 × 3, 3 × 2, and 4 × 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 σ = 1%. Calculate the volatility implied by Black's model for each option.