Multivariate Stochastic Volatility with Dynamic Cross Leverage

WA multivariate stochastic volatility (MSV) model based on a Cholesky-type decomposition of the covariance matrix to model dynamic correlation in the observation and transition error as well as in cross leverage terms is proposed. The empirically relevant asymmetric concept of cross leverage is defined as a nonzero correlation between the ith asset return at time t and the jth log-volatility at time t+1. Volatilities and covariances are modeled separately, which makes an interpretation of leverage parameters straightforward. The model is applied on a three-dimensional portfolio consisting of the S&P 500 sector indices Financials, Industrials and Healthcare, spanning the recent financial crisis 2008/09. During and in the aftermath of market turmoil, increased cross leverage effects, higher unconditional kurtosis and stronger correlated information flow are observed. However, there is risk of overfitting and restricting time variation to elements governing dynamics of the observation error may be advisable.