Multivariate Extreme Cvar Based on the D-Norm

Abstract

Measuring systemic risk is challenging in the presence of extreme events and tail dependence. This paper proposes an extension of Conditional Value-at-Risk based on Extreme Value Theory and D-norms. A multivariate excess aggregation variable is introduced through a D-norm, and its convergence to a Generalized Pareto Distribution is established. This framework preserves dependence structures and provides an analytical decomposition of systemic risk. Finally, a simulation study illustrates the theoretical results and the practical implementation of the proposed approach.