Forecasting Value-at-Risk using block structure multivariate stochastic volatility models

Most multivariate variance or volatility models suffer from a common problem, the “curse of dimensionality”. For this reason, most are fitted under strong parametric restrictions that reduce the interpretation and flexibility of the models. Recently, the literature has focused on multivariate models with milder restrictions, whose purpose is to combine the need for interpretability and efficiency faced by model users with the computational problems that may emerge when the number of assets can be very large. A contribution to this strand of the literature including a block-type parameterization for multivariate stochastic volatility models is provided. The empirical analysis on stock returns on the US market shows that 1% and 5% Value-at-Risk thresholds based on one-step-ahead forecasts of covariances by the new specification are satisfactory for the period including the Global Financial Crisis.