Multivariate stochastic volatility, leverage and news impact surfaces

Abstract

Alternative multivariate stochastic volatility (MSV) models with leverage have been proposed in the literature. However, the existing MSV with leverage models are unclear about the definition of leverage, specifically the timing of the relationship between the innovations in financial returns and the associated shocks to volatility, as well as their connection to partial correlations. This paper proposes a new MSV with leverage (MSVL) model in which leverage is defined clearly in terms of the innovations in both financial returns and volatility, such that the leverage effect associated with one financial return is not related to the leverage effect of another. News impact surfaces are developed for MSV models with leverage based on both log-volatility and volatility and are compared with the special case of news impact functions for their univariate counterparts. In order to capture heavy tails in each return distribution, we incorporate an additional factor for the volatility of each return. An empirical example based on bivariate data for Standard and Poor's 500 Composite Index and the Nikkei 225 Index is presented to illustrate the usefulness of the new MSVL model and the associated news impact surfaces. Likelihood ratio (LR) tests are considered for model selection. The LR tests show that the two-factor MSVL model is supported, indicating that the restrictions considered in the paper are empirically adequate under heavy-tailed return distributions.