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Equivalent Risk Indicators : VaR, TCE, and Beyond

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Listed:
  • Silvia Faroni
  • Olivier Le Courtois

    (EM - EMLyon Business School)

  • Krzysztof Ostaszewski

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," Post-Print hal-04325627, HAL.
    • Handle: RePEc:hal:journl:hal-04325627
    Note: View the original document on HAL open archive server: https://hal.science/hal-04325627
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    References listed on IDEAS

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    1. 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.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    3. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    4. 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.
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    Keywords

    VaR; TCE; extended TCE; Insurance regulation; Risk measurement;
    All these keywords.

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