Estimating the marginal contribution to systemic risk by a CoVaR-model based on copula functions and Extreme Value Theory

In this paper we quantify the contribution to systemic risk of a single financial institution by utilizing a analytical framework based on the principles of Extreme Value Theory (EVT) for modelling the marginal distributions and on the properties of copula functions for describing the dependence structure between the financial system and the single financial institution. Among the several systemic risk measures proposed nowadays by academics and estimated by public data, we choose to adopt as systemic risk metric the Conditional Value-at-Risk (CoVaR) by Adrian and Brunnermeier (2011) as well as the modified CoVaR notion by Girardi and Ergün (2013). We select a co-risk measure like the CoVaR because of its macro-dimension that allows us to integrate the dependence structure of the single financial institution and of the whole financial system in the systemic risk measurement. While the copula functions have been utilized in some pioneer studies on this area, in particular we follow the copula approach as described in Hakwa et al. (2015), the EVT principles have not yet been implemented in such a context of systemic risk contribution measurement.