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 e±cient 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.
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Paper provided by EconWPA in its series Finance with number
0502005.
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Raoul Pietersz & Marcel van Regenmortel, 2005.
"Generic Market Models,"
Finance
0502009, EconWPA.
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Other versions:
Pietersz, R. & Regenmortel, M. van, 2005.
"Generic Market Models,"
Research Paper
ERS-2005-010-F&A Revision, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
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