We present an approach that calculates the HW volatility to make the swaption price calculated on a HW tree match Black's price for the same swaption at each grid point. At each grid point, we compared respective Black’s and HW trinomial tree payer swaption pricing benchmarks. Specifically, using the interest rate and implied Black’s volatility.

We present a method for bootstrapping a set of zero rates from an input set of US government money market securities and bonds. We detail the calculations used to convert ACT/365 continuously compounded zero rates to the rates. We assume semi-annual compounding and, respectively, 30/360 and ACT/360 day-count fraction.

The payoff at maturity from a GIC can be shown equal to the invested principal plus this principal times the sum of the minimum guaranteed interest rate and the payoff from a European call option on the arithmetic average of the basket price, where the basket price is given by a weighted sum of the index levels.

The model estimates the swap price as a risk-neutral expectation of the difference between the bond price whose yield-to-maturity is the swap rate and the bond’s par. The swap rate is considered a log-normally distributed random variable.