Measuring risks in the extreme tail: The extreme VaR and its confidence interval

Dominique Guegan (), Bertrand K. Hassani () and Kehan Li ()
Additional contact information
Dominique Guegan: Centre d'Economie de la Sorbonne, https://cv.archives-ouvertes.fr/dominique-guegan
Bertrand K. Hassani: Grupo Santander et Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.univ-paris1.fr
Kehan Li: Centre d'Economie de la Sorbonne et Labex ReFi, https://centredeconomiesorbonne.univ-paris1.fr

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: Contrary to the current regulatory trend concerning extreme risks, the purpose of this paper is to emphasize the necessity of considering the Value-at-Risk (VaR) with extreme confidence levels like 99.9%, as an alternative way to measure risks in the “extreme tail”. Although the mathematical definition of the extreme VaR is trivial, its computation is challenging in practice, because the uncertainty of the extreme VaR may not be negligible for a finite amount of data. We begin to build confidence intervals around the unknown VaR. We build them using two different approaches, the first using Smirnov's result (Smirnov, 1949 [24]) and the second Zhu and Zhou's result (Zhu and Zhou, 2009 [25]), showing that this last one is robust when we use finite samples. We compare our approach with other methodologies which are based on bootstrapping techniques, Christoffersen et al. (2005) [7], focusing on the estimation of the extreme quantiles of a distribution. Finally, we apply these confidence intervals to perform a stress testing exercice with historical stock returns during financial crisis, for identifying potential violations of the VaR during turmoil periods on financial markets

Keywords: Regulation; Extreme risk; Extreme Value-at-Risk; Confidence interval; Asymptotic theory; Stress testing (search for similar items in EconPapers)
JEL-codes: C14 D81 G28 G32 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2016-04, Revised 2017-01
New Economics Papers: this item is included in nep-ore and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Journal Risk and Decision Analysis, IOS Press, vol 6, 2017, pages 213-224

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