Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions

This article proposes a new Bayesian Markov chain Monte Carlo (MCMC) methodology for estimation of a wide class of multidimensional jump-diffusion models. Our approach is based on the closed-form (CF) likelihood approximations of Aït-Sahalia (2002, 2008). The CF likelihood approximation does not integrate to 1; it is very close to 1 when in the center of the distribution but can differ markedly from 1 when far in the tails. We propose an MCMC algorithm that addresses the problems that arise when the CF approximation is applied in a Bayesian context. The efficacy of our approach is demonstrated in a simulation study of the Cox--Ingersoll--Ross and Heston models and is applied to two well-known datasets. Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.