Pricing Coupon Bond Options and Swaptions under the
Two-Factor Hull-White Model

Abstract

In this article, we propose an alternative approach for pricing bond options and swaptions under the two-factor Hull-White model that differs from existing models used to evaluate these instruments. Assuming that the forward price of a coupon bond is a martingale under the forward risk-neutral measure, the proposed model involves deriving the volatility of the coupon bond as a function of the stochastic durations calculated with respect to the model’s two factors. Once the volatility function is defined, the price of options on coupon bonds can be derived by simply applying standard no-arbitrage pricing theory. Given the equivalence between the price of a coupon bond and the price of the corresponding swaptions, our approach can be adopted to calibrate the parameters of the two-factor Hull-White model using swaptions quoted in the market. The new solution we propose for the calibration can be considered as an alternative with respect to the existing approaches proposed in the literature and currently used by practitioners. Numerical results are provided in order to analyze the features of the proposed model for calibration purposes.