Nonparametric Inference for Extreme CoVaR and CoES

TL;DR

This paper introduces nonparametric extrapolative methods for estimating extreme CoVaR and CoES, addressing inference challenges at high risk levels using tail dependence modeling and asymptotic theory, validated through simulations and real data.

Contribution

It proposes novel nonparametric extrapolative techniques for extreme CoVaR and CoES estimation within tail dependence frameworks, with rigorous asymptotic analysis.

Findings

Methods effectively estimate extreme CoVaR and CoES at high risk levels.

Simulation and real data analyses demonstrate superior empirical performance.

Asymptotic theories support the validity of the proposed estimators.

Abstract

Systemic risk measures quantify the potential risk to an individual financial constituent arising from the distress of entire financial system. As a generalization of two widely applied risk measures, Value-at-Risk and Expected Shortfall, the Conditional Value-at-Risk (CoVaR) and Conditional Expected Shortfall (CoES) have recently been receiving growing attention on applications in economics and finance, since they serve as crucial metrics for systemic risk measurement. However, existing approaches confront some challenges in statistical inference and asymptotic theories when estimating CoES, particularly at high risk levels. In this paper, within a framework of upper tail dependence, we propose several extrapolative methods to estimate both extreme CoVaR and CoES nonparametrically via an adjustment factor, which are intimately related to the nonparametric modelling of the tail dependence function. In addition, we study the asymptotic theories of all proposed extrapolative methods based on multivariate extreme value theory. Finally, some simulations and real data analyses are conducted to demonstrate the empirical performances of our methods.