Fast Drift Approximated Pricing in the Bgm Model

Journal of Computational Finance, Vol. 8, No. 1, 2004

34 Pages Posted: 26 Mar 2004 Last revised: 9 May 2011

See all articles by Raoul Pietersz

Raoul Pietersz

ABN AMRO

Antoon Pelsser

Maastricht University; Netspar

Marcel Van Regenmortel

ABN-Amro Bank, The Netherlands

Date Written: October 7, 2003

Abstract

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.

Keywords: BGM model, predictor-corrector, Brownian bridge, Markov processes, separability, Feynman-Kac, Bermudan swaption

JEL Classification: G13

Suggested Citation

Pietersz, Raoul and Pelsser, Antoon A. J. and Van Regenmortel, Marcel, Fast Drift Approximated Pricing in the Bgm Model (October 7, 2003). Journal of Computational Finance, Vol. 8, No. 1, 2004. Available at SSRN: https://ssrn.com/abstract=520424

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Marcel Van Regenmortel

ABN-Amro Bank, The Netherlands ( email )

NL-1000 EA Amsterdam
Netherlands

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