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Title: Impact of multimodality of distributions on VaR and ES calculations Authors:  Kehan Li - University Paris I Pantheon Sorbonne (France) [presenting]
Dominique Guegan - Universite Paris 1 - Pantheon-Sorbonne (France)
Bertrand Hassani - Université Paris 1 Pantheon Sorbonne - Labex Refi (France)
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. 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 with five minutes intraday data. With a complete spectrum of confidence levels from $0.001$ to $0.999$, we analyze the VaR and the ES to see the interest of using multimodal distribution instead of unimodal distribution.