Maximum likelihood estimation of stochastic volatility models

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 approximated 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.