期刊名称：Documents de Travail du Centre d'Economie de la Sorbonne
印刷版ISSN：1955-611X
出版年度：2017
出版社：Centre d'Economie de la Sorbonne
摘要：Contrary to the current regulatory trend concerning extreme risks, the purposeof this paper is to emphasize the necessity of considering the Value-at-Risk(VaR) with extreme con dence levels like 999%, as an alternative way to measurerisks in the \extreme tail". Although the mathematical de nition of theextreme VaR is trivial, its computation is challenging in practice, because theuncertainty of the extreme VaR may not be negligible for a nite amount of data.We begin to build con dence intervals around the unknown VaR.We build themusing two di erent approaches, the rst using Smirnov 's result (Smirnov, 1949[24]) and the second Zhu and Zhou 's result (Zhu and Zhou, 2009 [25]), showingthat this last one is robust when we use nite samples. We compare our approachwith other methodologies which are based on bootstrapping techniques,Christo ersen et al. (2005) [7], focusing on the estimation of the extreme quantilesof a distribution. Finally, we apply these con dence intervals to performa stress testing exercise with historical stock returns during nancial crisis, foridentifying potential violations of the VaR during turmoil periods on nancialmarkets.
