In the paper we analysis and compare the modelling ability of discrete-time Multivariate Stochastic Volatility models to describe the conditional correlations and volatilities of stock index returns. We consider four multivariate stochastic volatility models, including the specification with zero, constant and time-varying conditional correlations. These MSV specifications are used to model volatilities and conditional correlations between stock index returns. We study trivariate volatility models for the daily log returns on the WIG, S&P 500 and FTSE 100 indices for the period 4 January 1999 to 30 December 2005.

Given a model, inference about the volatilities and conditional correlations is based on the joint posterior distribution of the latent variables and the parameters, which we simulate via Markov chain Monte Carlo methods (the Metropolis-Hastings algorithm is used within the Gibbs sampler). Model comparison is fully Bayesian, based on Bayes factors obtained under proper prior densities for each model parameters.

The results indicate that the most adequate specifications are those that allow for time-varying conditional correlations and that have as many latent processes as there are conditional variances and covariances. The empirical results clearly show that the conditional correlations change over time and tend to be higher when markets are down trending.

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