Fragility Index of block tailed vectors

TL;DR

This paper extends the fragility index concept from multivariate extreme value theory to block-structured systems, providing new relations with tail dependence measures and applying the results to financial data to assess systemic stability.

Contribution

It generalizes the fragility index for block-structured systems and links it with existing tail dependence measures, offering new estimators and practical financial applications.

Findings

Derived relations between fragility index and tail dependence measures

Proposed estimators for systemic stability in block systems

Applied methodology to real financial data

Abstract

Financial crises are a recurrent phenomenon with important effects on the real economy. The financial system is inherently fragile and it is therefore of great importance to be able to measure and characterize its systemic stability. Multivariate extreme value theory provide us such a framework through the \emph{fragility index} (Geluk \cite{gel+}, \emph{et al.}, 2007; Falk and Tichy, \cite{falk+tichy1,falk+tichy2} 2010, 2011). Here we generalize this concept and contribute to the modeling of the stability of a stochastic system divided into blocks. We will find several relations with well-known tail dependence measures in literature, which will provide us immediate estimators. We end with an application to financial data.