Stochastic volatility with leverage: fast likelihood inference

Yasuhiro Omori: Faculty of Economics, University of Tokyo, Tokyo 113-0033, Japan omori@e.u-tokyo.ac.jp

Siddhartha Chib: Olin School of Business, Washington University, St Louis, USA chib@olin.wustl.edu

Neil Shephard: Nuffield College, Oxford OX1 1NF, UK neil.shephard@nuf.ox.ac.uk

Jouchi Nakajima: Faculty of Economics, University of Tokyo, Tokyo 113-0033, Japan n_sophia@f3.dion.ne.jp

Abstract

Kim, Shephard and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a very fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which limited its scope for applications. Despite this, their basic method has been extensively used in financial economics literature and more recently in macroeconometrics. In this paper we show how to overcome the limitation of this analysis so that the essence of the Kim, Shephard and Chib (1998) can be used to deal with the leverage effect, greatly extending the applicability of this method. Several illustrative examples are provided.  

Keywords: Leverage effect, Markov chain Monte Carlo, Mixture sampler, Stochastic volatility, Stock returns.

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