Dynamic CoVaR Modeling

The popular systemic risk measure CoVaR (conditional Value-at-Risk) is widely used in economics and finance. Formally, it is defined as an (extreme) quantile of one variable (e.g., losses in the financial system) conditional on some other variable (e.g., losses in a bank's shares) being in distress and, hence, measures the spillover of risks. In this article, we propose joint dynamic and semiparametric models for VaR and CoVaR together with a two-step M-estimator for the model parameters drawing on recently proposed bivariate scoring functions for the pair (VaR, CoVaR). Among others, this allows for the estimation of joint dynamic forecasting models for (VaR, CoVaR). We prove consistency and asymptotic normality of the proposed estimator and analyze its finite-sample properties in simulations. We apply our dynamic models to generate CoVaR forecasts for real financial data, which are shown to be superior to existing methods.