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Journal of Financial Econometrics Advance Access originally published online on June 7, 2007
Journal of Financial Econometrics 2007 5(3):390-455; doi:10.1093/jjfinec/nbm009
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Copyright © The Author 2007. Published by Oxford University Press.

Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

A. S. Hurn and J. I. Jeisman
     Queensland University of Technology

K. A. Lindsay
     University of Glasgow

Address correspondence to J. I. Jeisman, School of Economics and Finance, Queensland University of Technology, Brisbane, 4001, Australia, or e-mail: j.jeisman{at}qut.edu.au


  Abstract

Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This article provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox–Ingersoll–Ross and Ornstein–Uhlenbeck equations respectively.

KEYWORDS: stochastic differential equations, parameter estimation, maximum likelihood, simulation, moments

We are particularly grateful to Yacine Aït-Sahalia who read and commented on several earlier versions of this article. We would also like to thank Eric Renault, Adrian Pagan, Vance Martin, Ralf Becker, Kerrie Mengersen, Andrew Sanford, an associate editor, and two referees for useful comments. All remaining errors are the responsibility of the authors.

Received February 2, 2006; revised February 16, 2007; accepted April 26, 2007


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