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

Author

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  • 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
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    References listed on IDEAS

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    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    7. 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.
    8. 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.
    9. Dominique Guegan & Bertrand K. Hassani, 2018. "More accurate measurement for enhanced controls: VaR vs ES?," Post-Print halshs-01917569, HAL.
    10. Kerkhof, Jeroen & Melenberg, Bertrand, 2004. "Backtesting for risk-based regulatory capital," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1845-1865, August.
    11. 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.
    12. 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.
    13. 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.
    14. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 75, European Central Bank.
    15. William J. Baumol, 1963. "An Expected Gain-Confidence Limit Criterion for Portfolio Selection," Management Science, INFORMS, vol. 10(1), pages 174-182, October.
    16. Stefan Weber, 2006. "Distribution‐Invariant Risk Measures, Information, And Dynamic Consistency," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 419-441, April.
    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.
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