Pricing Bermudan Swaption under Two Factor Hull-White Model with Fast Gauss Transform

TL;DR

This paper introduces a fast, stable algorithm for pricing Bermudan swaptions under the two-factor Hull-White model, utilizing Gaussian kernel sums and the fast Gauss transform to significantly reduce computation time and improve stability.

Contribution

The paper develops a novel algorithm that combines numerical integration, Gaussian kernel sums, and the fast Gauss transform for efficient Bermudan swaption valuation under the two-factor Hull-White model.

Findings

Reduces computational complexity from O(N^2) to O(N)

Significantly decreases computation time in numerical experiments

Enhances stability when correlation is close to -1

Abstract

This paper describes a fast and stable algorithm for evaluating Bermudan swaption under the two factor Hull-White model. We discretize the calculation of the expected value in the evaluation of Bermudan swaption by numerical integration, and Gaussian kernel sums appears in it. The fast Gauss transform can be applied to these Gaussian kernel sums, and it reduces computational complexity from $O(N^2)$ to $O(N)$ as grid points number $N$ of numerical integration. We also propose to stabilize the computation under the condition that the correlation is close to $-1$ by introducing the grid rotation. Numerical experiments using actual market data show that our method reduces the computation time significantly compared to the method without the fast Gauss transform. They also show that the method of the grid rotation contributes to computational stability in the situations where the correlation is close to $-1$ and time step is short.