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Teaching an old dog new tricks: Improved estimation of the parameters of SDEs by numerical solution of the Fokker-Planck equation

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Author Info
Stan Hurn
J.Jeisman
K.A. Lindsay (School of Economics and Finance, Queensland University of Technology)

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Abstract

Many stochastic differential equations (SDEs) do not have readily available closed-form expressions for their transitional probability density functions (PDFs). As a result, a large number of competing estimation approaches have been proposed in order to obtain maximum-likelihood estimates of their parameters. Arguably the most straightforward of these is one in which the required estimates of the transitional PDF are obtained by numerical solution of the Fokker-Planck (or forward-Kolmogorov) partial differential equation. Despite the fact that this method produces accurate estimates and is completely generic, it has not proved popular in the applied literature. Perhaps this is attributable to the fact that this approach requires repeated solution of a parabolic partial differential equation to obtain the transitional PDF and is therefore computationally quite expensive. In this paper, three avenues for improving the reliability and speed of this estimation method are introduced and explored in the context of estimating the parameters of the popular Cox-Ingersoll-Ross and Ornstein-Uhlenbeck models. The recommended algorithm that emerges from this investigation is seen to offer substantial gains in reliability and computational time.

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Paper provided by School of Economics and Finance, Queensland University of Technology in its series Stan Hurn Discussion Papers with number 2006-01.

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Date of creation: 15 Jun 2006
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Handle: RePEc:qut:sthurn:2006-01

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Related research
Keywords: stochastic differential equations; maximum likelihood; finite difference; finite element; cumulative distribution function; interpolation.;

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