Measuring the Marginal Systemic Risk Contribution Using Copula

Abstract:     
In this paper we present a closed analytical formula for the calculation of the CoVaR (respectively Delta CoVaR), which is a macro risk measure introduced by Adrian and Brunnermeier to analyze and quantify the marginal contribution of a given financial institutions to the systemic risk. We derive a closed analytical expression of the CoVaR, by using a link between the conditional copula function and the CoVaR through their probabilistic interpretations. We conclude this article by applying our formula to compute CoVaR and Delta CoVaR in the Gaussian setting and presenting some interesting related results. We show that in the Gaussian framework the CoVaR and the Delta CoVaR may be expressed as a linear function of the value at risk of the corresponding singlefinancial institution.

Number of Pages in PDF File: 18

Keywords: Systemic Risk, Copula, CoVaR, Conditional Copula, Macro Risk Measure

JEL Classification: C00

working papers series