An efficient method for maximum likelihood estimation of a stochastic volatility model

In this paper an efficient, simulation-based, maximum likelihood (ML) method is proposed for estimating Taylor’s stochastic volatility (SV) model. The new method is based on the second order Taylor approximation to the integrand. The approximation enables us to transfer the numerical problem in the Laplace approximation and that in importance sampling into the problem of inverting two high dimensional symmetric tri-diagonal matrices. A result recently developed in the linear algebra literature shows that such an inversion has an analytic form, greatly facilitating the computations of the likelihood function of the SV model. In addition to provide parameter estimation, the new method offers an efficient way to filter, smooth, and forecast latent log-volatility. The new method is illustrated and compared with existing ML methods using simulated data. Results suggest that the proposed method greatly reduces the computational cost in estimation without sacrificing the statistical efficiency, at least for the parameter settings considered.

Keywords

maximum likelihood, stochastic volatility models, Laplace approximation, importance sampler

2010 Mathematics Subject Classification

Primary 62G05, 62G09. Secondary 62P20.

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Published 1 January 2008