Kendall Conditional Value-at-Risk

The Conditional Value-at-Risk (CoVaR) is a modified version of the Value-at-Risk (VaR) to quantify the risk of a random variable Y with respect to another random variable X. In this work, we consider a multivariate modification of CoVaR based on the Kendall distribution function. In particular, we discuss two possible hazard scenarios that generalize the standard CoVar and use the copula theory to derive the corresponding risk quantities. We consider a systemic risk exercise of the Italian banking system to demonstrate how the multivariate modification of CoVaR can be useful to analyze the resilience of a system when some parts of it are under distress.