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Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?

Author

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  • Laurent Devineau

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon, R&D, Milliman, Paris - Milliman France)

  • Stéphane Loisel

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

Two approaches may be considered in order to determine the Solvency II economic capital: the use of a standard formula or the use of an internal model (global or partial). However, the results produced by these two methods are rarely similar, since the underlying hypothesis of marginal capital aggregation is not verified by the projection models used by companies. We demonstrate that the standard formula can be considered as a first order approximation of the result of the internal model. We therefore propose an alternative method of aggregation that enables to satisfactorily capture the diversity among the various risks that are considered, and to converge the internal models and the standard formula.

Suggested Citation

  • Laurent Devineau & Stéphane Loisel, 2009. "Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?," Post-Print hal-00403662, HAL.
    • Handle: RePEc:hal:journl:hal-00403662
    Note: View the original document on HAL open archive server: https://hal.science/hal-00403662v2
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    References listed on IDEAS

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    1. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    2. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
    3. Wayne Fisher & Stéphane Loisel & Shaun Wang, 2008. "On some key research issues in Enterprise Risk Management related to economic capital and diversification effect at group level," Post-Print hal-00268841, HAL.
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    Cited by:

    1. Julien Vedani & Fabien Ramaharobandro, 2013. "Continuous compliance: a proxy-based monitoring framework," Papers 1309.7222, arXiv.org, revised Dec 2013.
    2. Marcel T. P. Van Dijk & Cornelis S. L. De Graaf & Cornelis W. Oosterlee, 2018. "Between ℙ and ℚ: The ℙ ℚ Measure for Pricing in Asset Liability Management," JRFM, MDPI, vol. 11(4), pages 1-23, October.
    3. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    4. Loisel, Stéphane & Milhaud, Xavier, 2011. "From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital," European Journal of Operational Research, Elsevier, vol. 214(2), pages 348-357, October.
    5. Matthieu Chauvigny & Laurent Devineau & Stéphane Loisel & Véronique Maume-Deschamps, 2011. "Fast remote but not extreme quantiles with multiple factors. Applications to Solvency II and Enterprise Risk Management," Post-Print hal-00517766, HAL.
    6. Fabrice Borel-Mathurin & Julien Vedani, 2019. "Market-consistent valuation: a step towards calculation stability," Working Papers hal-02282378, HAL.
    7. Julien Vedani & Laurent Devineau, 2012. "Solvency assessment within the ORSA framework: issues and quantitative methodologies," Papers 1210.6000, arXiv.org, revised Oct 2012.
    8. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    9. Mezőfi, Balázs & Niedermayer, Andras & Niedermayer, Daniel & Süli, Balázs Márton, 2017. "Solvency II reporting: How to interpret funds’ aggregate solvency capital requirement figures," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 164-171.
    10. Julien Vedani & Laurent Devineau, 2012. "Solvency assessment within the ORSA framework: issues and quantitative methodologies," Working Papers hal-00744351, HAL.
    11. Pauline Milaure Ngugnie Diffouo & Pierre Devolder, 2020. "Longevity Risk Measurement of Life Annuity Products," Risks, MDPI, vol. 8(1), pages 1-16, March.
    12. Asier Garayeta & J. Inaki De La Pena & Ivan Iturricastillo, 2014. "Pragmatic Solutions for Solvency Capital Requirements at Life Insurance Companies: The Case of Spain," International Journal of Business Administration, International Journal of Business Administration, Sciedu Press, vol. 5(4), pages 39-51, July.
    13. 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.
    14. Eling, Martin & Jung, Kwangmin, 2020. "Risk aggregation in non-life insurance: Standard models vs. internal models," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 183-198.
    15. Julien Vedani & Fabien Ramaharobandro, 2013. "Continuous compliance: a proxy-based monitoring framework," Working Papers hal-00866531, HAL.
    16. Xavier Milhaud & Victorien Poncelet & Clement Saillard, 2018. "Operational Choices for Risk Aggregation in Insurance: PSDization and SCR Sensitivity," Risks, MDPI, vol. 6(2), pages 1-23, April.

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