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Generating VaR Scenarios under Solvency II with Product Beta Distributions

Author

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  • Dietmar Pfeifer

    (School of Mathematics and Science, Institute of Mathematics, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany)

  • Olena Ragulina

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska Str., 01601 Kyiv, Ukraine)

Abstract

We propose a Monte Carlo simulation method to generate stress tests by VaR scenarios under Solvency II for dependent risks on the basis of observed data. This is of particular interest for the construction of Internal Models. The approach is based on former work on partition-of-unity copulas, however with a direct scenario estimation of the joint density by product beta distributions after a suitable transformation of the original data.

Suggested Citation

  • Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:4:p:122-:d:176564
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    References listed on IDEAS

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    1. Yang, Jingping & Chen, Zhijin & Wang, Fang & Wang, Ruodu, 2015. "Composite Bernstein Copulas," ASTIN Bulletin, Cambridge University Press, vol. 45(2), pages 445-475, May.
    2. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    3. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.
    4. Pfeifer Dietmar & Mändle Andreas & Ragulina Olena, 2017. "New copulas based on general partitions-of-unity and their applications to risk management (part II)," Dependence Modeling, De Gruyter, vol. 5(1), pages 246-255, October.
    5. Georg Mainik, 2015. "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions," Papers 1508.02749, arXiv.org.
    6. Pfeifer Dietmar & Tsatedem Hervé Awoumlac & Mändle Andreas & Girschig Côme, 2016. "New copulas based on general partitions-of-unity and their applications to risk management," Dependence Modeling, De Gruyter, vol. 4(1), pages 123-140, July.
    7. 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.
    8. Rustam Ibragimov & Artem Prokhorov, 2017. "Heavy Tails and Copulas:Topics in Dependence Modelling in Economics and Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9644.
    9. 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.
    10. Yannick Malevergne & Didier Sornette, 2006. "Extreme Financial Risks : From Dependence to Risk Management," Post-Print hal-02298069, HAL.
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    Citations

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    Cited by:

    1. Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    2. Solveig Flaig & Gero Junike, 2022. "Scenario Generation for Market Risk Models Using Generative Neural Networks," Risks, MDPI, vol. 10(11), pages 1-28, October.
    3. Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Papers 2011.00909, arXiv.org, revised Mar 2021.
    4. Solveig Flaig & Gero Junike, 2023. "Validation of machine learning based scenario generators," Papers 2301.12719, arXiv.org, revised Nov 2023.
    5. Dietmar Pfeifer & Olena Ragulina, 2020. "Generating unfavourable VaR scenarios with patchwork copulas," Papers 2011.06281, arXiv.org, revised May 2021.
    6. 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.
    7. Solveig Flaig & Gero Junike, 2021. "Scenario generation for market risk models using generative neural networks," Papers 2109.10072, arXiv.org, revised Aug 2023.

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