Fast drift-approximated pricing in the BGM model

It is demonstrated 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 that is especially designed to have high accuracy for single time stepping. The scheme is proven to converge weakly with order one. 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 by a factor 10, yet maintaining sufficiently accurate pricing.