Maximum Likelihood Estimation of Time-Inhomogeneous Diffusions

Posted: 17 Sep 2002

See all articles by Alexei V. Egorov

Alexei V. Egorov

West Virginia University - College of Business & Economics

Haitao Li

University of Michigan - Stephen M. Ross School of Business; Cheung Kong Graduate School of Business; Cheung Kong Graduate School of Business

Yuewu Xu

Teachers Insurance and Annuity Association College Retirement Equities Fund (TIAA-CREF)

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Abstract

We extend the maximum likelihood estimation method of Ait-Sahalia (2002) for time-homogeneous diffusions to time-inhomogeneous ones. We derive a closed-form approximation of the likelihood function for discretely sampled time-inhomogeneous diffusions, and prove that this approximation converges to the true likelihood function and yields consistent parameter estimates. Monte Carlo simulations for several financial models reveal that our method largely outperforms other widely used numerical procedures in approximating the likelihood function. Furthermore, parameter estimates produced by our method are very close to the parameter estimates obtained by maximizing the true likelihood function, and superior to estimates obtained from the Euler approximation.

Keywords: Maximum likelihood estimation, time-inhomogeneous diffusion, transition density, Hermite expansion

JEL Classification: C0, C1, C4, G0

Suggested Citation

Egorov, Alexei V. and Li, Haitao and Xu, Yuewu, Maximum Likelihood Estimation of Time-Inhomogeneous Diffusions. Available at SSRN: https://ssrn.com/abstract=331380

Alexei V. Egorov

West Virginia University - College of Business & Economics ( email )

Morgantown, WV 26506-6025
United States

Haitao Li (Contact Author)

University of Michigan - Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
734-615-5475 (Phone)

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Yuewu Xu

Teachers Insurance and Annuity Association College Retirement Equities Fund (TIAA-CREF) ( email )

730 Third Avenue
New York, NY 10017-3206
United States

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