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Generating unfavourable VaR scenarios under Solvency II with patchwork copulas

Author

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  • Pfeifer Dietmar

    (Carl von Ossietzky Universität Oldenburg, Germany)

  • Ragulina Olena

    (Taras Shevchenko National University of Kyiv, Ukraine)

Abstract

The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the European Union. Besides this, the Delegated Regulation by the European Commission requires all insurance companies under supervision to consider different risk scenarios in their risk management system for the company’s own risk assessment. Since it is unreasonable to assume that the potential worst case scenario will materialize in the company, we think that a modelling of various unfavourable scenarios as described in this paper is likewise appropriate. Our explicit copula approach can be considered as a special case of ordinal sums, which in two dimensions even leads to the technically worst VaR scenario.

Suggested Citation

  • Pfeifer Dietmar & Ragulina Olena, 2021. "Generating unfavourable VaR scenarios under Solvency II with patchwork copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 327-346, January.
    • Handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:327-346:n:2
    DOI: 10.1515/demo-2021-0115
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    References listed on IDEAS

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    1. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    2. Varnell, Elliot, 2011. "Economic Scenario Generators and Solvency II ‐ Abstract of the Discussion," British Actuarial Journal, Cambridge University Press, vol. 16(1), pages 161-179, May.
    3. Georg Mainik, 2015. "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions," Papers 1508.02749, arXiv.org.
    4. Mainik, Georg, 2015. "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 197-216.
    5. Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    6. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    7. 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.
    8. Varnell, E. M., 2011. "Economic Scenario Generators and Solvency II," British Actuarial Journal, Cambridge University Press, vol. 16(1), pages 121-159, May.
    9. Dietmar Pfeifer & Andreas Mandle & Olena Ragulina & C^ome Girschig, 2018. "New copulas based on general partitions-of-unity (part III) - the continuous case (extended version)," Papers 1803.00957, arXiv.org, revised May 2019.
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    Cited by:

    1. Yongzhao Chen & Ka Chun Cheung & Sheung Chi Phillip Yam & Fei Lung Yuen & Jia Zeng, 2023. "On the Diversification Effect in Solvency II for Extremely Dependent Risks," Risks, MDPI, vol. 11(8), pages 1-22, August.

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