A Multivariate Garch Model with Volatility Spill-Over and Time-Varying Correlations

Abstract

There is now a wide array of GARCH models available that are able to capture many important features of a univariate return time series. However, a lot of questions still remain open about which models are suitable for capturing the dynamics of multivariate return time series. This paper introduces a model for asset returns that incorporates joint heteroscedasticity as well as time varying correlations. It nests the model with cross-sectional volatility by Hwang and Satchell (2005) as well as the dynamical conditional correlation framework by Engle (2002).

We fit the model to ten years of data for stocks in the Dow Jones Industrial Average. The empirical results suggest that the average pairwise correlation behaves strongly countercyclical. This means that the benefits of diversification go down exactly when they are most desirable, which might serve as an explanation why the volatility smile in index options tends to be more pronounced than in individual stocks options.

Keywords: Dynamic Correlation, Multivariate GARCH, Volatility

JEL Classification: C32, G0, G1