IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/17019.html
   My bibliography  Save this paper

Impact of multimodality of distributions on VaR and ES calculations

Author

Listed:

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

Suggested Citation

  • Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Documents de travail du Centre d'Economie de la Sorbonne 17019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:17019
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2017/17019.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dominique Guégan & Bertrand Hassani, 2015. "Distortion Risk Measure or the Transformation of Unimodal Distributions into Multimodal Functions," International Series in Operations Research & Management Science, in: Alain Bensoussan & Dominique Guegan & Charles S. Tapiero (ed.), Future Perspectives in Risk Models and Finance, edition 127, pages 71-88, Springer.
    2. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. Bertrand K. Hassani & Wei Yang, 2016. "The Lila distribution and its applications in risk modelling," Documents de travail du Centre d'Economie de la Sorbonne 16068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Gao, Fuqing & Wang, Shaochen, 2011. "Asymptotic behavior of the empirical conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 345-352.
    6. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    7. Bertrand K. Hassani & Wei Yang, 2016. "The Lila distribution and its applications in risk modelling," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01400186, HAL.
    8. Bertrand K. Hassani & Wei Yang, 2016. "The Lila distribution and its applications in risk modelling," Post-Print halshs-01400186, HAL.
    9. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01491990, HAL.
    2. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Post-Print halshs-01491990, HAL.
    3. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    4. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
    5. Peña, Juan Ignacio & Rodríguez, Rosa & Mayoral, Silvia, 2020. "Tail risk of electricity futures," Energy Economics, Elsevier, vol. 91(C).
    6. repec:hal:journl:hal-00880258 is not listed on IDEAS
    7. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Documents de travail du Centre d'Economie de la Sorbonne 16034rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2017.
    8. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    9. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
    10. Righi, Marcelo Brutti & Borenstein, Denis, 2018. "A simulation comparison of risk measures for portfolio optimization," Finance Research Letters, Elsevier, vol. 24(C), pages 105-112.
    11. Kratz , Marie, 2013. "There is a VaR Beyond Usual Approximations," ESSEC Working Papers WP1317, ESSEC Research Center, ESSEC Business School.
    12. Marie Kratz, 2013. "There is a VaR Beyond Usual Approximations," Working Papers hal-00880258, HAL.
    13. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    14. Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    15. Fu, Tianwen & Zhuang, Xinkai & Hui, Yongchang & Liu, Jia, 2017. "Convex risk measures based on generalized lower deviation and their applications," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 27-37.
    16. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2015. "A comparison of Expected Shortfall estimation models," Journal of Economics and Business, Elsevier, vol. 78(C), pages 14-47.
    17. Sant’Anna, Leonardo Riegel & Righi, Marcelo Brutti & Müller, Fernanda Maria & Guedes, Pablo Cristini, 2022. "Risk measure index tracking model," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 361-383.
    18. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2017. "On a robust risk measurement approach for capital determination errors minimization," Papers 1707.09829, arXiv.org, revised Oct 2020.
    19. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    20. Iulia Lupu & Ana Barbara Bobirca & Paul Gabriel Miclaus & Tudor Ciumara, 2020. "Risk Management of Companies Included in the EURO STOXX Sustainability Index. An Investors' Perception," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 22(55), pages 707-707, August.
    21. Juan Ignacio Pe~na & Rosa Rodriguez & Silvia Mayoral, 2022. "Tail Risk of Electricity Futures," Papers 2202.01732, arXiv.org.

    More about this item

    Keywords

    Risks; Multimodal distributions; Value-at-Risk; Expected Shortfall; Moments method; Adapted rejection sampling; Regulation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:17019. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.