Stochastic volatility in mean: Efficient analysis by a generalized mixture sampler

Abstract

In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori et al. (2007), we develop an accurate approximation of the logarithm of the non-central chi-squared distribution as a mixture of thirty normal distributions. Under this mixture representation, we sample the parameters and latent volatilities in one block. We also detail a correction of the small approximation error by using additional Metropolis–Hastings steps. The proposed method is extended to the SVM model with leverage. The methodology and models are applied to excess holding yields and S&P500 returns in empirical studies, and the SVM models are shown to outperform other volatility models based on marginal likelihoods.