Bermudan Swaptions in Gaussian HJM One-Factor Model: Analytical and Numerical Approaches

Abstract

A popular way to value (Bermudan) swaption in a Hull-White or extended Vasicek model is to use a tree or PDE approach. A more direct approach through iterated numerical integration is developed. A brute force numerical integration would lead to a complexity exponential in the number of exercise dates in the base of the number of points (p^N). By carefully choosing the integration points and their order, the complexity can be reduced to 4pN versus the quadratic complexity (pN)^2 in the tree.

A semi-explicit formula leading to a faster converging implementation is also proposed.

Keywords: Bermudan option, swaption, Hull-White model, one-factor model, numerical integration

JEL Classification: G13, E43