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Equivalent Risk Indicators: VaR, TCE, and Beyond

Author

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  • Silvia Faroni

    (EMLyon Business School, 23, Avenue Guy de Collongue, CEDEX, 69134 Ecully, France
    COACTIS (EA4161), Université de Lyon/Lyon 2, ISH, 14-16 Avenue Berthelot, 69007 Lyon, France)

  • Olivier Le Courtois

    (EMLyon Business School, 23, Avenue Guy de Collongue, CEDEX, 69134 Ecully, France)

  • Krzysztof Ostaszewski

    (College of Arts and Science, Illinois State University (ISU), Normal, IL 61790-4520, USA)

Abstract

While a lot of research concentrates on the respective merits of VaR and TCE, which are the two most classic risk indicators used by financial institutions, little has been written on the equivalence between such indicators. Further, TCE, despite its merits, may not be the most accurate indicator to take into account the nature of probability distribution tails. In this paper, we introduce a new risk indicator that extends TCE to take into account higher-order risks. We compare the quantiles of this indicator to the quantiles of VaR in a simple Pareto framework, and then in a generalized Pareto framework. We also examine equivalence results between the quantiles of high-order TCEs.

Suggested Citation

  • Silvia Faroni & Olivier Le Courtois & Krzysztof Ostaszewski, 2022. "Equivalent Risk Indicators: VaR, TCE, and Beyond," Risks, MDPI, vol. 10(8), pages 1-19, July.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:8:p:142-:d:868713
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    References listed on IDEAS

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    1. PAVLO A. Krokhmal, 2007. "Higher moment coherent risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 373-387.
    2. Olivier Le Courtois & Christian Walter, 2014. "The Computation of Risk Budgets under the Lévy Process Assumption," Post-Print hal-01892836, HAL.
    3. Olivier Le Courtois, 2018. "Some Further Results on the Tempered Multistable Approach," Post-Print hal-02312142, HAL.
    4. Olivier Courtois, 2018. "Some Further Results on the Tempered Multistable Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(2), pages 87-109, June.
    5. Olivier Le Courtois & Christian Walter, 2014. "The Computation of Risk Budgets under the Lévy Process Assumption," Finance, Presses universitaires de Grenoble, vol. 35(2), pages 87-108.
    6. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    7. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    8. Thomas J. Linsmeier & Neil D. Pearson, 2000. "Value at Risk," Financial Analysts Journal, Taylor & Francis Journals, vol. 56(2), pages 47-67, March.
    9. 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.
    10. Sebastian Fuchs & Ruben Schlotter & Klaus D. Schmidt, 2017. "A Review and Some Complements on Quantile Risk Measures and Their Domain," Risks, MDPI, vol. 5(4), pages 1-16, November.
    11. Marzena Rostek, 2010. "Quantile Maximization in Decision Theory ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 339-371.
    12. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
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    Cited by:

    1. Annamaria Olivieri, 2023. "Special Issue “Actuarial Mathematics and Risk Management”," Risks, MDPI, vol. 11(7), pages 1-3, July.

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