This paper proposes and analyses two types of asymmetric multivariate stochastic
volatility (SV) models, namely: (i) SV with leverage (SV-L) model, which is based on
the negative correlation between the innovations in the returns and volatility; and (ii)
SV with leverage and size effect (SV-LSE) model, which is based on the signs and
magnitude of the returns. The paper derives the state space form for the logarithm of the squared returns which follow the multivariate SV-L model, and develops estimation methods for the multivariate SV-L and SV-LSE models based on the Monte Carlo likelihood (MCL) approach. The empirical results show that the multivariate SV-LSE model fits the bivariate and trivariate returns of the S&P 500, Nikkei 225, and Hang Seng indexes with respect to AIC and BIC more accurately than does the multivariate SV-L model. Moreover, the empirical results suggest that the univariate models should be rejected in favour of their bivariate and trivariate counterparts.