IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2142-d627907.html
   My bibliography  Save this article

Expected Shortfall Reliability—Added Value of Traditional Statistics and Advanced Artificial Intelligence for Market Risk Measurement Purposes

Author

Listed:
  • Santiago Carrillo Menéndez

    (Department of Mathematics, Science Faculty, Universitad Autonoma de Madrid, Carretera de Colmenar, Km. 15, Cantoblanco, 28049 Madrid, Spain
    QUANT AI Lab, C. de Arturo Soria, 122, 28043 Madrid, Spain)

  • Bertrand Kian Hassani

    (QUANT AI Lab, C. de Arturo Soria, 122, 28043 Madrid, Spain
    Department of Computer Science, University College London, Gower St, London WC1E 6EA, UK
    CES, MSE, Universite Panthéon Sorbonne, 106-112 Boulevard de l’Hôpital, 75013 Paris, France)

Abstract

The Fundamental Review of the Trading Book is a market risk measurement and management regulation recently issued by the Basel Committee. This reform, often referred to as “Basel IV”, intends to strengthen the financial system. The newest capital standard relies on the use of the Expected Shortfall. This risk measure requires to get sufficient information in the tails to ensure its reliability, as this one has to be alimented by a sufficient quantity of relevant data (above the 97.5 percentile in the case of the regulation or interest). In this paper, after discussing the relevant features of Expected Shortfall for risk measurement purposes, we present and compare several methods allowing to ensure the reliability of the risk measure by generating information in the tails. We discuss these approaches with respect to their relevance considering the underlying situation when it comes to available data, allowing practitioners to select the most appropriate approach. We apply traditional statistical methodologies, for instance distribution fitting, kernel density estimation, Gaussian mixtures and conditional fitting by Expectation-Maximisation as well as AI related strategies, for instance a Synthetic Minority Over-sampling Technique implemented in a regression environment and Generative Adversarial Nets.

Suggested Citation

  • Santiago Carrillo Menéndez & Bertrand Kian Hassani, 2021. "Expected Shortfall Reliability—Added Value of Traditional Statistics and Advanced Artificial Intelligence for Market Risk Measurement Purposes," Mathematics, MDPI, vol. 9(17), pages 1-20, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2142-:d:627907
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2142/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/17/2142/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dominique Guegan & Bertrand K. Hassani, 2018. "More accurate measurement for enhanced controls: VaR vs ES?," Post-Print halshs-01917569, HAL.
    2. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    3. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 75, European Central Bank.
    4. William J. Baumol, 1963. "An Expected Gain-Confidence Limit Criterion for Portfolio Selection," Management Science, INFORMS, vol. 10(1), pages 174-182, October.
    5. Stefan Weber, 2006. "Distribution‐Invariant Risk Measures, Information, And Dynamic Consistency," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 419-441, April.
    6. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    7. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
    8. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, vol. 4(2), pages 1-28, May.
    9. Dominique Guegan & Bertrand K. Hassani, 2018. "More accurate measurement for enhanced controls: VaR vs ES?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01917569, HAL.
    10. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    11. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    12. Ziggel, Daniel & Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2014. "A new set of improved Value-at-Risk backtests," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 29-41.
    13. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    14. Kerkhof, Jeroen & Melenberg, Bertrand, 2004. "Backtesting for risk-based regulatory capital," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1845-1865, August.
    15. Wong, Woon K., 2008. "Backtesting trading risk of commercial banks using expected shortfall," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1404-1415, July.
    16. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    17. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    18. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    19. Guegan, Dominique & Hassani, Bertrand K., 2018. "More accurate measurement for enhanced controls: VaR vs ES?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 54(C), pages 152-165.
    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. Sebastian Bayer & Timo Dimitriadis, 2022. "Regression-Based Expected Shortfall Backtesting [Backtesting Expected Shortfall]," Journal of Financial Econometrics, Oxford University Press, vol. 20(3), pages 437-471.
    2. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    3. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    4. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    5. Sebastian Bayer & Timo Dimitriadis, 2018. "Regression Based Expected Shortfall Backtesting," Papers 1801.04112, arXiv.org, revised Sep 2019.
    6. Kratz, Marie & Lok, Yen H. & McNeil, Alexander J., 2018. "Multinomial VaR backtests: A simple implicit approach to backtesting expected shortfall," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 393-407.
    7. Osmundsen, Kjartan Kloster, 2018. "Using expected shortfall for credit risk regulation," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 57(C), pages 80-93.
    8. Hamed Tabasi & Vahidreza Yousefi & Jolanta Tamošaitienė & Foroogh Ghasemi, 2019. "Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models," Administrative Sciences, MDPI, vol. 9(2), pages 1-17, May.
    9. Marie Kratz & Yen H Lok & Alexander J Mcneil, 2016. "Multinomial var backtests: A simple implicit approach to backtesting expected shortfall," Working Papers hal-01424279, HAL.
    10. Sander Barendse & Erik Kole & Dick van Dijk, 2023. "Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 528-568.
    11. Enrique Molina‐Muñoz & Andrés Mora‐Valencia & Javier Perote, 2021. "Backtesting expected shortfall for world stock index ETFs with extreme value theory and Gram–Charlier mixtures," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4163-4189, July.
    12. Tobias Fissler & Fangda Liu & Ruodu Wang & Linxiao Wei, 2024. "Elicitability and identifiability of tail risk measures," Papers 2404.14136, arXiv.org, revised Jun 2024.
    13. George Tzagkarakis & Frantz Maurer, 2020. "An energy-based measure for long-run horizon risk quantification," Annals of Operations Research, Springer, vol. 289(2), pages 363-390, June.
    14. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
    15. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    16. Kratz, Marie & Lok, Y-H & McNeil, Alexander J., 2016. "Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfall," ESSEC Working Papers WP1617, ESSEC Research Center, ESSEC Business School.
    17. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Risk quantification for commodity ETFs: Backtesting value-at-risk and expected shortfall," International Review of Financial Analysis, Elsevier, vol. 70(C).
    18. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    19. Ruodu Wang & Yunran Wei, 2020. "Risk functionals with convex level sets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1337-1367, October.
    20. Fissler Tobias & Ziegel Johanna F., 2021. "On the elicitability of range value at risk," Statistics & Risk Modeling, De Gruyter, vol. 38(1-2), pages 25-46, January.

    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:gam:jmathe:v:9:y:2021:i:17:p:2142-:d:627907. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.