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Scenario-based risk evaluation

Author

Listed:
  • Ruodu Wang

    (University of Waterloo)

  • Johanna F. Ziegel

    (University of Bern)

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 establish axiomatic characterisations of scenario-based risk measures that are comonotonic-additive or coherent, and we obtain a novel ES-based representation result. We propose several novel scenario-based risk measures, including various versions of Max-ES and Max-VaR, and study their properties. The theory is illustrated with financial data examples.

Suggested Citation

  • Ruodu Wang & Johanna F. Ziegel, 2021. "Scenario-based risk evaluation," Finance and Stochastics, Springer, vol. 25(4), pages 725-756, October.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:4:d:10.1007_s00780-021-00460-9
    DOI: 10.1007/s00780-021-00460-9
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    References listed on IDEAS

    as
    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Jie Shen & Yi Shen & Bin Wang & Ruodu Wang, 2019. "Distributional compatibility for change of measures," Finance and Stochastics, Springer, vol. 23(3), pages 761-794, July.
    4. Luting Li & Hao Xing, 2018. "Capital allocation under the Fundamental Review of Trading Book," Papers 1801.07358, arXiv.org, revised Jan 2019.
    5. Duffie, Darrell & Scheicher, Martin & Vuillemey, Guillaume, 2015. "Central clearing and collateral demand," Journal of Financial Economics, Elsevier, vol. 116(2), pages 237-256.
    6. Paul Embrechts & Haiyan Liu & Tiantian Mao & Ruodu Wang, 2017. "Quantile-Based Risk Sharing with Heterogeneous Beliefs," Swiss Finance Institute Research Paper Series 17-65, Swiss Finance Institute, revised Jan 2018.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Viral Acharya & Robert Engle & Matthew Richardson, 2012. "Capital Shortfall: A New Approach to Ranking and Regulating Systemic Risks," American Economic Review, American Economic Association, vol. 102(3), pages 59-64, May.
    9. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    10. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    11. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    12. Paul Embrechts & Giovanni Puccetti & Ludger Rüschendorf & Ruodu Wang & Antonela Beleraj, 2014. "An Academic Response to Basel 3.5," Risks, MDPI, vol. 2(1), pages 1-24, February.
    13. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
    14. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2017. "Domains of weak continuity of statistical functionals with a view toward robust statistics," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 1-19.
    15. 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.
    16. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    17. repec:dau:papers:123456789/342 is not listed on IDEAS
    18. Steven Kou & Xianhua Peng & Chris C. Heyde, 2013. "External Risk Measures and Basel Accords," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 393-417, August.
    19. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    20. Mathieu Cambou & Damir Filipović, 2017. "Model Uncertainty And Scenario Aggregation," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 534-567, April.
    21. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    22. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    23. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Citations

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    Cited by:

    1. Hirbod Assa & Peng Liu, 2024. "Factor risk measures," Papers 2404.08475, arXiv.org.
    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. 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.
    4. Yi Shen & Zachary Van Oosten & Ruodu Wang, 2024. "Partial Law Invariance and Risk Measures," Papers 2401.17265, arXiv.org, revised Jun 2024.
    5. Fabio Bellini & Tiantian Mao & Ruodu Wang & Qinyu Wu, 2024. "Disappointment concordance and duet expectiles," Papers 2404.17751, arXiv.org, revised Oct 2024.
    6. 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).
    7. 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.
    8. Tolulope Fadina & Yang Liu & Ruodu Wang, 2021. "A Framework for Measures of Risk under Uncertainty," Papers 2110.10792, arXiv.org, revised Sep 2023.
    9. Felix-Benedikt Liebrich, 2021. "Risk sharing under heterogeneous beliefs without convexity," Papers 2108.05791, arXiv.org, revised May 2022.
    10. Ruodu Wang & Zhenyuan Zhang, 2022. "Simultaneous Optimal Transport," Papers 2201.03483, arXiv.org, revised May 2023.
    11. Dejian Tian & Xunlian Wang, 2023. "Dynamic star-shaped risk measures and $g$-expectations," Papers 2305.02481, arXiv.org.

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    More about this item

    Keywords

    Scenarios; Risk measures; Basel Accords; Stress adjustment; Dependence adjustment;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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