Analyzing Systemic Risk using CoVaR under Elliptical Distributions

One of the main challenges for the regulatory authorities in the aftermath of the last financial crisis is to define pragmatical and practicable risk concepts for the control and the regulation of systemic risks. They need for this purpose risk models that on one hand can capture the macro dimension of systemic risk, and on the other hand can be easily implemented and audited. The concept of consideration of the CoVaR under elliptical distribution is a reasonable Trade-off. Elliptical distributions have the particularity that they share many of the analytical properties of the multivariate normal distribution, but are flexible enough to model extreme co-movements as those observed during the last financial crisis. Furthermore, the quantitative risk-management techniques based on elliptical distributions are well-studied and in general consistent with the regulatory recommendations. This paper presents a closed form-formula for the computation of CoVaR when the relevant variables assume elliptical distributions. This approach generalizes the work of Jäger-Ambrozewicz [2010], where a close form formula for CoVaR under normal distribution is provided