Modeling Time-Varying Tail Dependence, with Application to Systemic Risk Forecasting*

Abstract

Empirical evidence for multivariate stock suggests that there are changes from asymptotic independence to asymptotic dependence and vice versa. Under asymptotic independence, the probability of joint extremes vanishes, whereas under asymptotic dependence, this probability remains positive. In this paper, we propose a dynamic model for bivariate extremes that allows for smooth transitions between regimes of asymptotic independence and asymptotic dependence. In doing so, we ignore the bulk of the distribution and only model the joint tail of interest. We propose a maximum-likelihood estimator for the model parameters and demonstrate its accuracy in simulations. An empirical application to losses on the CAC 40 and DAX 30 illustrates that our model provides a detailed description of changes in the extremal dependence structure. Furthermore, we show that our model issues adequate forecasts of systemic risk, as measured by CoVaR. Finally, we find some evidence that our CoVaR forecasts outperform those of a benchmark dynamic t-copula model.returns