Impact of multimodality of distributions on VaR and ES calculations

Dominique Guegan (), Bertrand Hassani () and Kehan Li ()
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Dominique Guegan: Centre d'Economie de la Sorbonne and LabEx ReFi, https://cv.archives-ouvertes.fr/dominique-guegan
Bertrand Hassani: Grupo Santander and Centre d'Economie de la Sorbonne and LabEx ReFi
Kehan Li: Centre d'Economie de la Sorbonne and LabEx ReFi

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

Abstract: Unimodal probability distribution has been widely used for Value-at-Risk (VaR) computation by investors, risk managers and regulators. However, financial data may be characterized by distributions having more than one modes. Using a unimodal distribution may lead to bias for risk measure computation. In this paper, we discuss the influence of using multimodal distributions on VaR and Expected Shortfall (ES) calculation. Two multimodal distribution families are considered: Cobb's family and distortion family. We provide two ways to compute the VaR and the ES for them: an adapted rejection sampling technique for Cobb's family and an inversion approach for distortion family. For empirical study, two data sets are considered: a daily data set concerning operational risk and a three month scenario of market portfolio return built five minutes intraday data. With a complete spectrum of confidence levels from 0001 to 0.999, we analyze the VaR and the ES to see the interest of using multimodal distribution instead of unimodal distribution

Keywords: Risks; Multimodal distributions; Value-at-Risk; Expected Shortfall; Moments method; Adapted rejection sampling; Regulation (search for similar items in EconPapers)
JEL-codes: C13 C15 G28 G32 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2017-03
New Economics Papers: this item is included in nep-ban and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:17019

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