Impact of multimodality of distributions on VaR and ES calculations

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.
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Documents de travail du Centre d'Economie de la Sorbonne 2017.19 - ISSN : 1955-611X. 2017
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Soumis le : vendredi 17 mars 2017 - 17:09:07
Dernière modification le : samedi 18 mars 2017 - 01:11:42

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Dominique Guegan, Bertrand Hassani, Kehan Li. Impact of multimodality of distributions on VaR and ES calculations. Documents de travail du Centre d'Economie de la Sorbonne 2017.19 - ISSN : 1955-611X. 2017. <halshs-01491990>

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