IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2312.13195.html

Principal Component Copulas for Capital Modelling and Systemic Risk

Author

Listed:
  • K. B. Gubbels
  • J. Y. Ypma
  • C. W. Oosterlee

Abstract

We introduce a class of copulas that we call Principal Component Copulas (PCCs). This class combines the strong points of copula-based techniques with principal component analysis (PCA), which results in flexibility when modelling tail dependence along the most important directions in high-dimensional data. We obtain theoretical results for PCCs that are important for practical applications. In particular, we derive tractable expressions for the high-dimensional copula density, which can be represented in terms of characteristic functions. We also develop algorithms to perform Maximum Likelihood and Generalized Method of Moment estimation in high-dimensions and show very good performance in simulation experiments. Finally, we apply the copula to the international stock market to study systemic risk. We find that PCCs lead to excellent performance on measures of systemic risk due to their ability to distinguish between parallel and orthogonal movements in the global market, which have a different impact on systemic risk and diversification. As a result, we consider the PCC promising for capital models, which financial institutions use to protect themselves against systemic risk.

Suggested Citation

  • K. B. Gubbels & J. Y. Ypma & C. W. Oosterlee, 2023. "Principal Component Copulas for Capital Modelling and Systemic Risk," Papers 2312.13195, arXiv.org, revised Jul 2025.
    • Handle: RePEc:arx:papers:2312.13195
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2312.13195
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Fang Duan & Hans Manner & Dominik Wied, 2022. "Model and Moment Selection in Factor Copula Models [Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings]," Journal of Financial Econometrics, Oxford University Press, vol. 20(1), pages 45-75.
    4. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    5. Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    6. L. A. Grzelak & J. A. S. Witteveen & M. Suárez-Taboada & C. W. Oosterlee, 2019. "The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions," Quantitative Finance, Taylor & Francis Journals, vol. 19(2), pages 339-356, February.
    7. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
    8. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    9. Oh, Dong Hwan & Patton, Andrew J., 2023. "Dynamic factor copula models with estimated cluster assignments," Journal of Econometrics, Elsevier, vol. 237(2).
    10. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Koos B. Gubbels & Andre Lucas, 2026. "Spectral Dynamics and Regularization for High-Dimensional Copulas," Papers 2601.13281, arXiv.org.

    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. Javier Ojea Ferreiro, 2025. "A Market-Based Approach to Reverse Stress Testing the Financial System," Staff Working Papers 25-32, Bank of Canada.
    2. Nguyen, Hoang & Virbickaitė, Audronė & Ausín, M. Concepción & Galeano, Pedro, 2024. "Structured factor copulas for modeling the systemic risk of European and United States banks," International Review of Financial Analysis, Elsevier, vol. 96(PA).
    3. Jialing Han & Yu-Ning Li, 2025. "Approximate Factor Model with S-vine Copula Structure," Papers 2508.11619, arXiv.org.
    4. Tong, Chen & Hansen, Peter Reinhard, 2023. "Characterizing correlation matrices that admit a clustered factor representation," Economics Letters, Elsevier, vol. 233(C).
    5. Chen Tong & Peter Reinhard Hansen, 2025. "Dynamic Factor Correlation Model," Papers 2503.01080, arXiv.org.
    6. Manner, Hans & Stark, Florian & Wied, Dominik, 2019. "Testing for structural breaks in factor copula models," Journal of Econometrics, Elsevier, vol. 208(2), pages 324-345.
    7. Nguyen, Hoang & Ausín, M. Concepción & Galeano, Pedro, 2020. "Variational inference for high dimensional structured factor copulas," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    8. Müller, Dominik & Czado, Claudia, 2019. "Dependence modelling in ultra high dimensions with vine copulas and the Graphical Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 211-232.
    9. Kreuzer, Alexander & Czado, Claudia, 2021. "Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 130-150.
    10. Eugen Ivanov & Aleksey Min & Franz Ramsauer, 2017. "Copula-Based Factor Models for Multivariate Asset Returns," Econometrics, MDPI, vol. 5(2), pages 1-24, May.
    11. Quanrui Song & Jianxu Liu & Songsak Sriboonchitta, 2019. "Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    12. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    13. Bartels, Mariana & Ziegelmann, Flavio A., 2016. "Market risk forecasting for high dimensional portfolios via factor copulas with GAS dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 66-79.
    14. Koos B. Gubbels & Andre Lucas, 2026. "Spectral Dynamics and Regularization for High-Dimensional Copulas," Papers 2601.13281, arXiv.org.
    15. Hua, Lei & Joe, Harry, 2017. "Multivariate dependence modeling based on comonotonic factors," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 317-333.
    16. Ackerer Damien & Vatter Thibault, 2017. "Dependent defaults and losses with factor copula models," Dependence Modeling, De Gruyter, vol. 5(1), pages 375-399, December.
    17. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    18. Verhoijsen Alex & Krupskiy Pavel, 2022. "Fast inference methods for high-dimensional factor copulas," Dependence Modeling, De Gruyter, vol. 10(1), pages 270-289, January.
    19. Damien Ackerer & Thibault Vatter, 2016. "Dependent Defaults and Losses with Factor Copula Models," Papers 1610.03050, arXiv.org, revised Jan 2018.
    20. Tachibana, Minoru, 2022. "Safe haven assets for international stock markets: A regime-switching factor copula approach," Research in International Business and Finance, Elsevier, vol. 60(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2312.13195. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.