Globally Optimal Parameter Estimates for Non-Linear Diffusions

26 Pages Posted: 19 Mar 2008 Last revised: 14 May 2009

See all articles by Aleksandar Mijatovic

Aleksandar Mijatovic

Imperial College London

Paul Schneider

University of Lugano - Institute of Finance; Swiss Finance Institute

Date Written: January 1, 2008

Abstract

This paper studies an approximation method for the log likelihood function of a non-linear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The approach is applicable to a subclass of non-linear SDEs with constant volatility and drift that is linear in the model parameters. In this setting globally optimal parameters are obtained in a single step by solving a square linear system whose dimension equals the number of parameters in the model. Simulation studies to test the EML algorithm show that it performs well when compared with algorithms based on the exact maximum likelihood as well as closed-form likelihood expansions.

Keywords: Maximum likelihood, global optimization, non-linear diffusion, EM algorithm, estimation

JEL Classification: C13, C15

Suggested Citation

Mijatovic, Aleksandar and Schneider, Paul Georg, Globally Optimal Parameter Estimates for Non-Linear Diffusions (January 1, 2008). Available at SSRN: https://ssrn.com/abstract=1109002 or http://dx.doi.org/10.2139/ssrn.1109002

Aleksandar Mijatovic

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/a.mijatovic

Paul Georg Schneider (Contact Author)

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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