Fast Drift Approximated Pricing in the Bgm Model

Raoul Pietersz, Antoon Pelsser, Marcel van Regenmortel

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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.
Original languageEnglish
Pages (from-to)93-124
JournalJournal of Computational Finance
Volume8
Issue number1
DOIs
Publication statusPublished - 2004
Externally publishedYes

JEL classifications

  • g13 - "Contingent Pricing; Futures Pricing; option pricing"

Keywords

  • BGM model
  • predictor-corrector
  • Brownian bridge
  • Markov processes
  • seperability
  • Feynman-Kac
  • Bermudan swaption

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