* Corresponding author. E-mail: s.j.koopman@kub.nl Journal of Econometrics 87 (1998) 271 — 301 Estimation of stochastic volatility models via Monte Carlo maximum likelihood Gleb Sandmann, Siem Jan Koopman*  Financial Markets Group, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK  CentER for Economic Research, Tilburg University, 5000 LE Tilburg, Netherlands Received 1 September 1996; received in revised form 1 October 1997 Abstract This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chi-square disturbances. The likelihood function can be approxi- mated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favorably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Monte Carlo Markov chain (MCMC) method.  1998 Elsevier Science S.A. All rights reserved. JEL classification: C15; C22 Keywords: GARCH model; Importance sampling; Kalman filter smoother; Monte Carlo simulation; Quasi-maximum likelihood; Stochastic Volatility; Unobserved components 1. Introduction The empirical distributions of financial time series differ substantially from distributions obtained from sampling independent homoskedastic Gaussian variables. Unconditional density functions exhibit leptokurtosis and skewness; 0304-4076/98/$ — see front matter  1998 Elsevier Science S.A. All rights reserved. PII S 0304-4076(98)00016-5