CoVaR under Asymptotic Independence

Conditional value-at-risk (CoVaR) is one of the most important measures of systemic risk. It is defined as the high quantile conditional on a related variable being extreme, widely used in the field of quantitative risk management. In this work, we develop a semi-parametric methodology to estimate CoVaR for asymptotically independent pairs within the framework of bivariate extreme value theory. We use parametric modelling of the bivariate extremal structure to address data sparsity in the joint tail regions and prove consistency and asymptotic normality of the proposed estimator. The robust performance of the estimator is illustrated via simulation studies. Its application to the US stock returns data produces insightful dynamic CoVaR forecasts.