A new non-parametric estimation of the expected shortfall for dependent financial losses

Second Author's Department

Economics Department

Find in your Library

https://doi.org/10.1016/j.jspi.2024.106151

All Authors

Khouzeima Moutanabbir, Mohammed Bouaddi

Document Type

Research Article

Publication Title

Journal of Statistical Planning and Inference

Publication Date

9-1-2024

doi

10.1016/j.jspi.2024.106151

Abstract

In this paper, we address the problem of kernel estimation of the Expected Shortfall (ES) risk measure for financial losses that satisfy the α-mixing conditions. First, we introduce a new non-parametric estimator for the ES measure using a kernel estimation. Given that the ES measure is the sum of the Value-at-Risk and the mean-excess function, we provide an estimation of the ES as a sum of the estimators of these two components. Our new estimator has a closed-form expression that depends on the choice of the kernel smoothing function, and we derive these expressions in the case of Gaussian, Uniform, and Epanechnikov kernel functions. We study the asymptotic properties of this new estimator and compare it to the Scaillet estimator. Capitalizing on the properties of these two estimators, we combine them to create a new estimator for the ES which reduces the bias and lowers the mean square error. The combined estimator shows better stability with respect to the choice of the kernel smoothing parameter. Our findings are illustrated through some numerical examples that help us to assess the small sample properties of the different estimators considered in this paper.

This document is currently not available here.

Find this item online

Share

COinS