Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study

In this paper, we make two contributions to the MSV literature. First, we propose two new MSV models that account for leverage effects. Second, we compare the small sample performances of Quasi Maximum Likelihood (QML) and Monte Carlo Likelihood (MCL) methods through Monte Carlo studies for Constant Correlations MSV and Time Varying Correlations MSV and for the two MSV models with leverage we propose. We also provide the specific transformations necessary for the MCL estimation of the proposed MSV models with leverage. Our results confirm that the MCL estimator has better small sample performance compared to the QML estimator. In terms of parameter estimation, both estimators perform better when the series are highly correlated. In estimating the underlying volatilities and correlations, QML estimator's performance comes closer to that of MCL estimator when the SV process has higher variance or when the correlations are time varying, while it is performing relatively worse in MSV models with leverage. Finally we include an empirical illustration by estimating an MSV model with leverage that we propose using a trivariate data from the major European stock markets.