A Note on the Statistical Robustness of Risk Measures

22 Pages Posted: 14 Jun 2017

See all articles by Mikhail Zhelonkin

Mikhail Zhelonkin

Erasmus University Rotterdam (EUR)

Valérie Chavez-Demoulin

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne)

Date Written: June 13, 2017

Abstract

The question of robustness in risk measurement emerged only fairly recently, but it has already attracted considerable attention. The problem has been studied using various approaches, and several methods aiming at robustifying the risk measures have been proposed. However, a general robustness theory is still missing. We focus on the parametric estimators of risk measures and use Hampel’s infinitesimal approach to derive the robustness properties. We derive the influence functions for the general parametric estimators of the value-at-risk and expected shortfall. For various distributions, the classical estimators, such as maximum likelihood, have unbounded influence functions and are not robust. Using the expression for the influence function, we propose a general strategy to construct robust estimators and explore their properties. The use of the methodology is demonstrated through several illustrative examples. Finally, we discuss an operational risk application and highlight the importance of the complementary information provided by nonrobust and robust estimates for regulatory capital calculation.

Keywords: expected shortfall (ES), influence function, M-estimation, risk measures, robustness, value-at-risk (VaR)

Suggested Citation

Zhelonkin, Mikhail and Chavez-Demoulin, Valérie, A Note on the Statistical Robustness of Risk Measures (June 13, 2017). Journal of Operational Risk, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2985428

Mikhail Zhelonkin

Erasmus University Rotterdam (EUR) ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

Valérie Chavez-Demoulin (Contact Author)

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Anthropole
Lausanne, 1015
Switzerland

HOME PAGE: http://https://www.hec.unil.ch/people/vchavez&vue=contact&set_language=en&cl=en

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