Fast Drift Approximated Pricing in the Bgm Model

This paper shows that the forward rates process discretized by a single time step together with a separability assumption on the volatility function allows for representation by a low-dimensional Markov process. This in turn leads to efficient pricing by for example finite differences. We then develop a discretization based on the Brownian bridge especially designed to have high accuracy for single time stepping. The scheme is proven to converge weakly with order 1. We compare the single time step method for pricing on a grid with multi step Monte Carlo simulation for a Bermudan swaption, reporting a computational speed increase of a factor 10, yet pricing sufficiently accurate.