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Adaptive Bernstein Copulas and Risk Management

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  • Dietmar Pfeifer
  • Olena Ragulina

Abstract

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas w.r.t. the estimation of risk measures in risk management.

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  • Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Papers 2011.00909, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2011.00909
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    References listed on IDEAS

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    1. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 35-51.
    2. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    3. Berghaus, Betina & Segers, Johan, 2017. "Weak convergence of the weighted empirical beta copula process," LIDAM Discussion Papers ISBA 2017015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Zhong Guan, 2016. "Efficient and robust density estimation using Bernstein type polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 250-271, June.
    5. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
    6. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    7. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    8. Zhong Guan, 2017. "Bernstein polynomial model for grouped continuous data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 831-848, October.
    9. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," LIDAM Reprints ISBA 2017005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    1. Dietmar Pfeifer & Olena Ragulina, 2020. "Generating unfavourable VaR scenarios with patchwork copulas," Papers 2011.06281, arXiv.org, revised May 2021.

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