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Principal Component Copulas for Capital Modelling and Systemic Risk

K. B. Gubbels, J. Y. Ypma, C. W. Oosterlee

arXiv 20 Dec 2023 · Finance — Risk Management · publishedComputational Economics (2025) · 1 citations (OpenAlex)

arXiv:2312.13195 · PDF · DOI · OpenAlex · Extracted main text

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.

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31
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1D. W. Oh and A. J. Patton (2017) Modeling dependence in high dimensions with factor copulas1.000124100%
2D. H. Oh and A.J. Patton (2023) Dynamic factor copula models with estimated cluster assignments1.00053100%
3A. Opschoor, A. Lucas, I. Barra, and D. Van Dijk (2021) Closed-form multi-factor copula models with observation-driven dynamic factor loadings1.00053100%
4F. Fang and C. W. Oosterlee (2009) A novel pricing method for european options based on fourier-cosine series expansions0.92844100%
5A. Lucas, B. Schwaab, and X. Zhang (2014) Conditional euro area sovereign default risk0.92843100%
6A.J. McNeil, R. Frey, and P. Embrechts (2005) Quantitative Risk Management0.92843100%
7S. Demarta and A.J. McNeil (2005) The t copula and related copulas0.87452100%
8P. Carr and D. Madan (1999) Option valuation using the fast fourier transform0.84333100%
9R. Ouyang, X. Chen, Y. Fang, and Y. Zhao (2022) Systemic risk of commodity markets: A dynamic factor copula approach0.81142100%
10J. Bun, J.-P. Bouchaud, and M. Potters (2017) Cleaning large correlation matrices: Tools from random matrix theory0.73732100%

Showing the top 10 of 31 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Spectral Dynamics and Regularization for High-Dimensional Copulas0.40511