Modeling Dependence and Risk in High Dimensions with Static and Dynamic Factor Copulas

In this study we examine multiple models for the dependence structure (copulas) of economic variables based on a latent factor structure. We differentiate between three types of copulas, allowing for a degree of time-varying dependence in increasing order: static, block-dynamic and GAS-dynamic copulas. After an extensive simulation study, the models are applied to daily returns on 50 constituents of the S&P 100 index. We compare various static and dynamic dependence models by their ability to create risk forecasts for the Value at Risk (VaR) and Expected Shortfall (ES). We find significant evidence of asymmetric dependence and tail dependence, implying that dependence is stronger during crises than in booms. We also show that factor copula models provide superior estimates of some risk measures, with the Skew t −t factor copula being most consistent.