CoVaR under Asymptotic Independence

TL;DR

This paper introduces a semi-parametric method for estimating CoVaR in asymptotically independent pairs, addressing data sparsity in joint tail regions within bivariate extreme value theory, with proven consistency and practical US stock data application.

Contribution

It develops a novel semi-parametric estimator for CoVaR under asymptotic independence, combining parametric extremal modeling with theoretical guarantees.

Findings

Estimator shows robust performance in simulations.

Application to US stock data yields insightful CoVaR forecasts.

Proves consistency and asymptotic normality of the estimator.

Abstract

Conditional value-at-risk (CoVaR) is one of the most important measures of systemic risk. It is defined as the high quantile conditional on a related variable being extreme, widely used in the field of quantitative risk management. In this work, we develop a semi-parametric methodology to estimate CoVaR for asymptotically independent pairs within the framework of bivariate extreme value theory. We use parametric modelling of the bivariate extremal structure to address data sparsity in the joint tail regions and prove consistency and asymptotic normality of the proposed estimator. The robust performance of the estimator is illustrated via simulation studies. Its application to the US stock returns data produces insightful dynamic CoVaR forecasts.