Extreme tail risk estimation with the generalized Pareto distribution under the peaks-over-threshold framework

Abstract

Modeling excesses over a high threshold and estimating extreme tail risk are two utmost studies in the extreme value literature. Traditional techniques are limited on handling these two challenges. To better analyze this type of data, we propose a novel approach which utilizes the generalized Pareto distribution (GPD) in the peaks-over-threshold (POT) framework. Under the proposed approach, by using partial L-moments (PL-moments), computational efficient estimators are derived for the parameters in the GPD. Additionally, we propose method to estimate the tail expectiles and apply a recently developed stopping rule to find the optimal threshold. Various simulation researches show that the proposed approach outperforms the traditional techniques in some aspects. Last, we apply the proposed method to the Shanghai Stock Exchange data for comprehensively illustrating the details and providing guidance for future applications.

Keywords:

• Threshold
• value at risk (VaR)
• expectiles
• peaks-over-threshold
• extreme values

Acknowledgments

The authors are very grateful to the editor and anonymous reviewers for their insightful and constructive comments and suggestions.

Additional information

Funding

The authors gratefully acknowledge the support of National Natural Science Foundation of China through Grant No. 11801019, Science and Technology Program of Beijing Education Commission through Grant No. KM201610005020.