Tail Gini Functional under Asymptotic Independence

TL;DR

This paper develops a method to estimate the tail Gini functional, a measure of tail risk variability, under asymptotic independence, with proven asymptotic normality and practical application to stock market risk analysis.

Contribution

It introduces a novel estimation approach for the tail Gini functional under asymptotic independence, including extrapolation to extreme tails and asymptotic properties.

Findings

Estimator performs well in bias and variance

Application reveals meaningful risk variability insights

Method applicable to systemic risk measurement

Abstract

Tail Gini functional is a measure of tail risk variability for systemic risks, and has many applications in banking, finance and insurance. Meanwhile, there is growing attention on aymptotic independent pairs in quantitative risk management. This paper addresses the estimation of the tail Gini functional under asymptotic independence. We first estimate the tail Gini functional at an intermediate level and then extrapolate it to the extreme tails. The asymptotic normalities of both the intermediate and extreme estimators are established. The simulation study shows that our estimator performs comparatively well in view of both bias and variance. The application to measure the tail variability of weekly loss of individual stocks given the occurence of extreme events in the market index in Hong Kong Stock Exchange provides meaningful results, and leads to new insights in risk management.