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Systemic Risk Modeling with Lévy Copulas

Author

Listed:
  • Yuhao Liu

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA
    Current address: Light Engineering, Stony Brook, NY 11790, USA.
    These authors contributed equally to this work.)

  • Petar M. Djurić

    (Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11794, USA
    These authors contributed equally to this work.)

  • Young Shin Kim

    (College of Business, Stony Brook University, Stony Brook, NY 11794, USA
    These authors contributed equally to this work.)

  • Svetlozar T. Rachev

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
    These authors contributed equally to this work.)

  • James Glimm

    (GlimmAnalyitcs, Port Jefferson, NY 11777, USA)

Abstract

We investigate a systemic risk measure known as CoVaR that represents the value-at-risk (VaR) of a financial system conditional on an institution being under distress. For characterizing and estimating CoVaR, we use the copula approach and introduce the normal tempered stable (NTS) copula based on the Lévy process. We also propose a novel backtesting method for CoVaR by a joint distribution correction. We test the proposed NTS model on the daily S&P 500 index and Dow Jones index with in-sample and out-of-sample tests. The results show that the NTS copula outperforms traditional copulas in the accuracy of both tail dependence and marginal processes modeling.

Suggested Citation

  • Yuhao Liu & Petar M. Djurić & Young Shin Kim & Svetlozar T. Rachev & James Glimm, 2021. "Systemic Risk Modeling with Lévy Copulas," JRFM, MDPI, vol. 14(6), pages 1-20, June.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:6:p:251-:d:569413
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    References listed on IDEAS

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    Cited by:

    1. Young Shin Kim & Frank J. Fabozzi, 2024. "Portfolio optimization with relative tail risk," Annals of Operations Research, Springer, vol. 341(2), pages 1023-1055, October.
    2. Dimuthu Fernando & Mohammed Alqawba & Manar Samad & Norou Diawara, 2022. "Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-52, November.
    3. Dimuthu Fernando & Mohammed Alqawba & Manar Samad & Norou Diawara, 2022. "Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-28, November.
    4. Young Shin Kim, 2023. "Portfolio Optimization with Relative Tail Risk," Papers 2303.12209, arXiv.org, revised Mar 2023.
    5. Bianchi, Michele Leonardo & De Luca, Giovanni & Rivieccio, Giorgia, 2023. "Non-Gaussian models for CoVaR estimation," International Journal of Forecasting, Elsevier, vol. 39(1), pages 391-404.

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