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The Solvency II square-root formula for systematic biometric risk

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  • Christiansen, Marcus C.
  • Denuit, Michel M.
  • Lazar, Dorina

Abstract

In this paper, we develop a model supporting the so-called square-root formula used in Solvency II to aggregate the modular life SCR. Describing the insurance policy by a Markov jump process, we can obtain expressions similar to the square-root formula in Solvency II by means of limited expansions around the best estimate. Numerical illustrations are given, based on German population data. Even if the square-root formula can be supported by theoretical considerations, it is shown that the QIS correlation matrix is highly questionable.

Suggested Citation

  • Christiansen, Marcus C. & Denuit, Michel M. & Lazar, Dorina, 2012. "The Solvency II square-root formula for systematic biometric risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 257-265.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:2:p:257-265
    DOI: 10.1016/j.insmatheco.2011.11.008
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    References listed on IDEAS

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    1. Renshaw, A. E. & Haberman, S., 2000. "Modelling the recent time trends in UK permanent health insurance recovery, mortality and claim inception transition intensities," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 365-396, December.
    2. Christiansen, Marcus C., 2008. "A sensitivity analysis concept for life insurance with respect to a valuation basis of infinite dimension," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 680-690, April.
    3. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    4. Katja Hanewald, 2011. "Explaining Mortality Dynamics," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 290-314.
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    Cited by:

    1. 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.
    2. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    3. 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.
    4. Gatzert, Nadine & Martin, Michael, 2012. "Quantifying credit and market risk under Solvency II: Standard approach versus internal model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 649-666.
    5. Djehiche, Boualem & Löfdahl, Björn, 2014. "Risk aggregation and stochastic claims reserving in disability insurance," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 100-108.
    6. Andreas Niemeyer, 2015. "Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework," Risks, MDPI, vol. 3(1), pages 1-26, January.
    7. Eling, Martin & Pankoke, David, 2013. "Basis Risk, Procylicality, and Systemic Risk in the Solvency II Equity Risk Module," Working Papers on Finance 1306, University of St. Gallen, School of Finance.
    8. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    9. Christiansen, Marcus C. & Niemeyer, Andreas & Teigiszerová, Lucia, 2015. "Modeling and forecasting duration-dependent mortality rates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 65-81.
    10. Michael Heinrich & Thomas Schreck, 2017. "Effects of Solvency II on Portfolio Efficiency, The Case of Real Estate and Infrastructure Investments," LARES lares_2017_paper_8, Latin American Real Estate Society (LARES).
    11. Boualem Djehiche & Björn Löfdahl, 2021. "Quantum Support Vector Regression for Disability Insurance," Risks, MDPI, vol. 9(12), pages 1-9, December.

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