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Scenario-based Risk Evaluation

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  • Ruodu Wang
  • Johanna F. Ziegel

Abstract

Risk measures such as Expected Shortfall (ES) and Value-at-Risk (VaR) have been prominent in banking regulation and financial risk management. Motivated by practical considerations in the assessment and management of risks, including tractability, scenario relevance and robustness, we consider theoretical properties of scenario-based risk evaluation. We propose several novel scenario-based risk measures, including various versions of Max-ES and Max-VaR, and study their properties. We establish axiomatic characterizations of scenario-based risk measures that are comonotonic-additive or coherent and an ES-based representation result is obtained. These results provide a theoretical foundation for the recent Basel III & IV market risk calculation formulas. We illustrate the theory with financial data examples.

Suggested Citation

  • Ruodu Wang & Johanna F. Ziegel, 2018. "Scenario-based Risk Evaluation," Papers 1808.07339, arXiv.org, revised May 2021.
    • Handle: RePEc:arx:papers:1808.07339
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Righi, Marcelo Brutti & Müller, Fernanda Maria & Moresco, Marlon Ruoso, 2020. "On a robust risk measurement approach for capital determination errors minimization," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 199-211.
    2. Gloria González‐Rivera & C. Vladimir Rodríguez‐Caballero & Esther Ruiz, 2024. "Expecting the unexpected: Stressed scenarios for economic growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 926-942, August.
    3. Yi Shen & Zachary Van Oosten & Ruodu Wang, 2024. "Partial Law Invariance and Risk Measures," Papers 2401.17265, arXiv.org, revised Jun 2024.
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    5. Shuo Gong & Yijun Hu & Linxiao Wei, 2022. "Distortion risk measures in random environments: construction and axiomatic characterization," Papers 2211.00520, arXiv.org, revised Mar 2023.
    6. Hirbod Assa & Peng Liu, 2024. "Factor risk measures," Papers 2404.08475, arXiv.org.
    7. Dejian Tian & Xunlian Wang, 2023. "Dynamic star-shaped risk measures and $g$-expectations," Papers 2305.02481, arXiv.org.
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    9. Tolulope Fadina & Yang Liu & Ruodu Wang, 2021. "A Framework for Measures of Risk under Uncertainty," Papers 2110.10792, arXiv.org, revised Sep 2023.
    10. Shuo Gong & Yijun Hu & Linxiao Wei, 2022. "Risk measurement of joint risk of portfolios: a liquidity shortfall aspect," Papers 2212.04848, arXiv.org, revised May 2024.
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    12. Nendel, Max & Streicher, Jan, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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