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...

We provide a detailed summary of the large and vibrant emerging literature that deals with the multivariate modeling of conditional volatility of financial time series within the framework of stochastic volatility. The developments and achievements in this area represent one of the great success...