An Efficient Numerical Method for Pricing Interest Rate Swaptions

It is not possible to directly apply integral transform and fast Fourier transform (FFT) theory to the problem of interest rate swaption pricing due to the nonaffine model dynamics assumed for the swap rate and underlying factor processes, defined under an equivalent swap measure. However, drawing from a recent result in the fixed-income literature, approximate, affine model dynamics are derived for a family of well-known affine models by replacing identified low-variance martingales with their martingale values. This allows the use of standard integral transform techniques in the pricing of interest-rate swaption contracts. The contribution of this chapter is primarily numerical, the main objective of which is to develop a computationally efficient swaption-pricing technology using fast Fourier transform methods. The pricing algorithms developed will greatly facilitate future empirical research into testing the goodness of fit of underlying term-structure models and in evaluating the dynamic hedging performance of various derivative-pricing models—topics of considerable interest among academics and practitioners alike.