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Multivariate Shortfall Risk Allocation and Systemic Risk

Author

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  • Yannick Armenti

    (LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique)

  • Stéphane Crépey

    (LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique)

  • Samuel Drapeau

    (Shanghai Jiao Tong University [Shanghai])

  • Antonis Papapantoleon

    (TUB - Technical University of Berlin / Technische Universität Berlin)

Abstract

The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the computation of an overall reserve level and its allocation to the different components according to their systemic relevance. We develop here a pragmatic approach to systemic risk measurement and allocation based on multivariate shortfall risk measures, where acceptable allocations are first computed and then aggregated so as to minimize costs. We analyze the sensitivity of the risk allocations to various factors and highlight its relevance as an indicator of systemic risk. In particular, we study the interplay between the loss function and the dependence structure of the components. Moreover, we address the computational aspects of risk allocation. Finally, we apply this methodology to the allocation of the default fund of a CCP on real data.

Suggested Citation

  • Yannick Armenti & Stéphane Crépey & Samuel Drapeau & Antonis Papapantoleon, 2018. "Multivariate Shortfall Risk Allocation and Systemic Risk," Working Papers hal-01764398, HAL.
    • Handle: RePEc:hal:wpaper:hal-01764398
    Note: View the original document on HAL open archive server: https://hal.science/hal-01764398
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    References listed on IDEAS

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    Cited by:

    1. Yichen Feng & Ming Min & Jean-Pierre Fouque, 2022. "Deep Learning for Systemic Risk Measures," Papers 2207.00739, arXiv.org.
    2. Alessandro Doldi & Marco Frittelli, 2021. "Real-Valued Systemic Risk Measures," Mathematics, MDPI, vol. 9(9), pages 1-24, April.
    3. Matteo Burzoni & Marco Frittelli & Federico Zorzi, 2021. "Robust market-adjusted systemic risk measures," Papers 2103.02920, arXiv.org, revised Aug 2021.
    4. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    5. Zachary Feinstein & Birgit Rudloff, 2018. "Time consistency for scalar multivariate risk measures," Papers 1810.04978, arXiv.org, revised Nov 2021.
    6. Albanese Claudio & Armenti Yannick & Crépey Stéphane, 2020. "XVA metrics for CCP optimization," Statistics & Risk Modeling, De Gruyter, vol. 37(1-2), pages 25-53, January.
    7. Alessandro Doldi & Marco Frittelli, 2020. "Conditional Systemic Risk Measures," Papers 2010.11515, arXiv.org, revised May 2021.
    8. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2023. "Are Shortfall Systemic Risk Measures One Dimensional?," Papers 2306.10752, arXiv.org.
    9. Francesca Biagini & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2020. "On fairness of systemic risk measures," Finance and Stochastics, Springer, vol. 24(2), pages 513-564, April.
    10. Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    11. Maria Arduca & Pablo Koch-Medina & Cosimo Munari, 2019. "Dual representations for systemic risk measures based on acceptance sets," Papers 1906.10933, arXiv.org, revised Oct 2019.
    12. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.
    13. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    14. Tathagata Banerjee & Zachary Feinstein, 2018. "Pricing of debt and equity in a financial network with comonotonic endowments," Papers 1810.01372, arXiv.org, revised Sep 2021.
    15. Ariah Klages-Mundt & Andreea Minca, 2021. "Optimal Intervention in Economic Networks using Influence Maximization Methods," Papers 2102.01800, arXiv.org, revised Mar 2023.
    16. Klages-Mundt, Ariah & Minca, Andreea, 2022. "Optimal intervention in economic networks using influence maximization methods," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1136-1148.
    17. Wissam AlAli & c{C}au{g}{i}n Ararat, 2024. "Systemic values-at-risk and their sample-average approximations," Papers 2408.08511, arXiv.org.
    18. Cosimo Munari, 2021. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Finance and Stochastics, Springer, vol. 25(1), pages 77-99, January.
    19. Yichen Feng & Jean-Pierre Fouque & Ruimeng Hu & Tomoyuki Ichiba, 2022. "Systemic Risk Models for Disjoint and Overlapping Groups with Equilibrium Strategies," Papers 2202.00662, arXiv.org.
    20. Tomasz R. Bielecki & Igor Cialenco & Shibi Feng, 2018. "A Dynamic Model Of Central Counterparty Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-34, December.
    21. E. Kromer & L. Overbeck & K. Zilch, 2019. "Dynamic systemic risk measures for bounded discrete time processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 77-108, August.
    22. Nils Detering & Thilo Meyer-Brandis & Konstantinos Panagiotou & Daniel Ritter, 2020. "Suffocating Fire Sales," Papers 2006.08110, arXiv.org, revised Nov 2021.
    23. Tobias Fissler & Jana Hlavinová & Birgit Rudloff, 2021. "Elicitability and identifiability of set-valued measures of systemic risk," Finance and Stochastics, Springer, vol. 25(1), pages 133-165, January.
    24. Alessandro Doldi & Marco Frittelli, 2019. "Multivariate Systemic Optimal Risk Transfer Equilibrium," Papers 1912.12226, arXiv.org, revised Oct 2021.
    25. Samuel Drapeau & Mekonnen Tadese, 2019. "Relative Bound and Asymptotic Comparison of Expectile with Respect to Expected Shortfall," Papers 1906.09729, arXiv.org, revised Jun 2020.

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    Keywords

    Systemic risk; risk allocation; multivariate shortfall risk; sensitivities; numerical methods; CCP default fund;
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