Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in “Handbook of Financial Time Series” (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss and T. Mikosch), 365-400. Springer-Verlag: New York. April 2009. )

Abstract

The success of univariate stochastic volatility (SV) models in relation to univariate GARCH models has spurred an enormous interest in generalizations of SV models to a multivariate setting. A large number of multivariate SV (MSV) models are now available along with clearly articulated estimation recipes. Our goal in this paper is to provide the first detailed summary of the various model formulations, along with connections and differences, and discuss how the models are estimated. We aim to show that the developments and achievements in this area represent one of the great success stories of financial econometrics.