IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v10y2022i9p180-d909068.html
   My bibliography  Save this article

Multi-Variate Risk Measures under Wasserstein Barycenter

Author

Listed:
  • M. Andrea Arias-Serna

    (Faculty of Engineering, University of Medellin, Medellin 050026, Colombia
    These authors contributed equally to this work.)

  • Jean Michel Loubes

    (Institut de Mathématiques de Toulouse, University of Toulouse, 31062 Toulouse, France
    These authors contributed equally to this work.)

  • Francisco J. Caro-Lopera

    (Faculty of Basic Sciences, University of Medellin, Medellin 050026, Colombia
    These authors contributed equally to this work.)

Abstract

When the uni-variate risk measure analysis is generalized into the multi-variate setting, many complex theoretical and applied problems arise, and therefore the mathematical models used for risk quantification usually present model risk. As a result, regulators have started to require that the internal models used by financial institutions are more precise. For this task, we propose a novel multi-variate risk measure, based on the notion of the Wasserstein barycenter. The proposed approach robustly characterizes the company’s exposure, filtering the partial information available from individual sources into an aggregate risk measure, providing an easily computable estimation of the total risk incurred. The new approach allows effective computation of Wasserstein barycenter risk measures in any location–scatter family, including the Gaussian case. In such cases, the Wasserstein barycenter Value-at-Risk belongs to the same family, thus it is characterized just by its mean and deviation. It is important to highlight that the proposed risk measure is expressed in closed analytic forms which facilitate its use in day-to-day risk management. The performance of the new multi-variate risk measures is illustrated in United States market indices of high volatility during the global financial crisis (2008) and during the COVID-19 pandemic situation, showing that the proposed approach provides the best forecasts of risk measures not only for “normal periods”, but also for periods of high volatility.

Suggested Citation

  • M. Andrea Arias-Serna & Jean Michel Loubes & Francisco J. Caro-Lopera, 2022. "Multi-Variate Risk Measures under Wasserstein Barycenter," Risks, MDPI, vol. 10(9), pages 1-15, September.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:9:p:180-:d:909068
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/10/9/180/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/10/9/180/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jianping Li & Xiaoqian Zhu & Cheng-Few Lee & Dengsheng Wu & Jichuang Feng & Yong Shi, 2015. "On the aggregation of credit, market and operational risks," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 161-189, January.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. Andrea Arias-Serna & Jean-Michel Loubes & Francisco J. Caro-Lopera, 2020. "Risk Measures Estimation Under Wasserstein Barycenter," Papers 2008.05824, arXiv.org.
    2. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    3. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    4. Tobias Fissler & Yannick Hoga, 2024. "How to Compare Copula Forecasts?," Papers 2410.04165, arXiv.org.
    5. Masahiko Egami & Rusudan Kevkhishvili, 2020. "Time reversal and last passage time of diffusions with applications to credit risk management," Finance and Stochastics, Springer, vol. 24(3), pages 795-825, July.
    6. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Yang, Xinda, 2021. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 9-24.
    7. Pfeifer Dietmar & Mändle Andreas & Ragulina Olena, 2017. "New copulas based on general partitions-of-unity and their applications to risk management (part II)," Dependence Modeling, De Gruyter, vol. 5(1), pages 246-255, October.
    8. Diba Daraei & Kristina Sendova, 2024. "Determining Safe Withdrawal Rates for Post-Retirement via a Ruin-Theory Approach," Risks, MDPI, vol. 12(4), pages 1-21, April.
    9. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    10. Nevrla, Matěj, 2020. "Systemic risk in European financial and energy sectors: Dynamic factor copula approach," Economic Systems, Elsevier, vol. 44(4).
    11. H. Kaibuchi & Y. Kawasaki & G. Stupfler, 2022. "GARCH-UGH: a bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 22(7), pages 1277-1294, July.
    12. Battulga Gankhuu, 2022. "Merton's Default Risk Model for Private Company," Papers 2208.01974, arXiv.org.
    13. Ansari Jonathan & Rockel Marcus, 2024. "Dependence properties of bivariate copula families," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-36.
    14. Stephan Schlüter & Fabian Menz & Milena Kojić & Petar Mitić & Aida Hanić, 2022. "A Novel Approach to Generate Hourly Photovoltaic Power Scenarios," Sustainability, MDPI, vol. 14(8), pages 1-16, April.
    15. Borowska, Agnieszka & Hoogerheide, Lennart & Koopman, Siem Jan & van Dijk, Herman K., 2020. "Partially censored posterior for robust and efficient risk evaluation," Journal of Econometrics, Elsevier, vol. 217(2), pages 335-355.
    16. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    17. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    18. Gorgi, P. & Koopman, S.J., 2023. "Beta observation-driven models with exogenous regressors: A joint analysis of realized correlation and leverage effects," Journal of Econometrics, Elsevier, vol. 237(2).
    19. Dimitris Bertsimas & Agni Orfanoudaki, 2021. "Algorithmic Insurance," Papers 2106.00839, arXiv.org, revised Dec 2022.
    20. Xuehai Zhang, 2019. "Value at Risk and Expected Shortfall under General Semi-parametric GARCH models," Working Papers CIE 123, Paderborn University, CIE Center for International Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:10:y:2022:i:9:p:180-:d:909068. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.