How accurate are modern Value-at-Risk estimators derived from extreme value theory?

  • Benjamin Mögel
  • Benjamin R. Auer
Original Research


In this study, we compare the out-of-sample forecasting performance of several modern Value-at-Risk (VaR) estimators derived from extreme value theory (EVT). Specifically, in a multi-asset study covering 30 years of stock, bond, commodity and currency market data, we analyse the accuracy of the classic generalised Pareto peak over threshold approach and three recently proposed methods based on the Box–Cox transformation, L-moment estimation and the Johnson system of distributions. We find that, in their unconditional form, some of the estimators may be acceptable under current regulatory assessment rules but none of them can continuously pass more advanced tests of forecasting accuracy. In their conditional forms, forecasting power is significantly increased and the Box–Cox method proves to be the most promising estimator. However, it is also important to stress that the traditional historical simulation approach, which is currently the most frequently used VaR estimator in commercial banks, can not only keep up with the EVT-based methods but occasionally even outperforms them (depending on the setting: unconditional versus conditional). Thus, recent claims to generally replace this simple method by theoretically more advanced EVT-based methods may be premature.


Value-at-Risk Extreme value theory Historical simulation Backtest Financial crisis 

JEL Classification

G10 G11 G17 



We thank an anonymous reviewer for valuable comments and suggestions. Generous financial support was provided by the Deutsche Bundesbank (Hauptverwaltung in Sachsen und Thüringen).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and Animals rights

Our research does not involve human participants and/or animals.

Informed consent

Informed consent is not relevant in the context of our study.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of FinanceUniversity of LeipzigLeipzigGermany
  2. 2.Chair of Financial ServicesUniversity of BremenBremenGermany
  3. 3.Research Network Area Macro, Money and International FinanceCESifo MunichMunichGermany

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