arXiv subjects

Qingzhao Zhong

Publications and source records attributed to Qingzhao Zhong.

3 recordsLinked to original sources

arXiv2026

Estimations of Extreme CoVaR and CoES under Asymptotic Independence

The two popular systemic risk measures CoVaR (Conditional Value-at-Risk) and CoES (Conditional Expected Shortfall) have recently been receiving growing attention on applications in economics and finance. In this paper, we study the estimations of extreme CoVaR and CoES when the two random variables are asymptotic independent but positively associated. We propose two types of extrapolative approaches: the first relies on intermediate VaR and extrapolates it to extreme CoVaR/CoES via an adjustment factor; the second directly extrapolates the estimated intermediate CoVaR/CoES to the extreme tails. All estimators, including both intermediate and extreme ones, are shown to be asymptotically normal. Finally, we explore the empirical performances of our methods through conducting a series of Monte Carlo simulations and a real data analysis on S&P500 Index with 12 constituent stock data.

stat.ME↗

arXiv2025

Nonparametric Inference for Extreme CoVaR and CoES

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.

stat.ME↗

arXiv2024

Tail Risk Equivalent Level Transition and Its Application for Estimating Extreme $L_p$-quantiles

$L_p$-quantile has recently been receiving growing attention in risk management since it has desirable properties as a risk measure and is a generalization of two widely applied risk measures, Value-at-Risk and Expectile. The statistical methodology for $L_p$-quantile is not only feasible but also straightforward to implement as it represents a specific form of M-quantile using $p$-power loss function. In this paper, we introduce the concept of Tail Risk Equivalent Level Transition (TRELT) to capture changes in tail risk when we make a risk transition between two $L_p$-quantiles. TRELT is motivated by PELVE in Li and Wang (2023) but for tail risk. As it remains unknown in theory how this transition works, we investigate the existence, uniqueness, and asymptotic properties of TRELT (as well as dual TRELT) for $L_p$-quantiles. In addition, we study the inference methods for TRELT and extreme $L_p$-quantiles by using this risk transition, which turns out to be a novel extrapolation method in extreme value theory. The asymptotic properties of the proposed estimators are established, and both simulation studies and real data analysis are conducted to demonstrate their empirical performance.

stat.ME↗