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.

翻译：条件风险价值（CoVaR）是衡量系统性风险最重要的指标之一，其定义为在相关变量处于极端条件下对应的高分位数，在量化风险管理领域被广泛使用。本研究基于二元极值理论框架，针对渐近独立变量对提出了一种估计CoVaR的半参数方法。我们采用二元极值结构的参数化建模来解决联合尾部区域的数据稀疏性问题，并证明了所提估计量的一致性与渐近正态性。通过模拟研究验证了该估计量的稳健性能。将其应用于美国股票收益率数据，得到了具有洞察力的动态CoVaR预测结果。