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A full and synthetic model for Asset-Liability Management in life insurance, and analysis of the SCR with the standard formula


  • Aur'elien Alfonsi
  • Adel Cherchali
  • Jose Arturo Infante Acevedo


The aim of this paper is to introduce a synthetic ALM model that catches the main specificity of life insurance contracts. First, it keeps track of both market and book values to apply the regulatory profit sharing rule. Second, it introduces a determination of the crediting rate to policyholders that is close to the practice and is a trade-off between the regulatory rate, a competitor rate and the available profits. Third, it considers an investment in bonds that enables to match a part of the cash outflow due to surrenders, while avoiding to store the trading history. We use this model to evaluate the Solvency Capital Requirement (SCR) with the standard formula, and show that the choice of the interest rate model is important to get a meaningful model after the regulatory shocks on the interest rate. We discuss the different values of the SCR modules first in a framework with moderate interest rates using the shocks of the present legislation, and then we consider a low interest framework with the latest recommandation of the EIOPA on the shocks. In both cases, we illustrate the importance of matching cash-flows and its impact on the SCR.

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  • Aur'elien Alfonsi & Adel Cherchali & Jose Arturo Infante Acevedo, 2019. "A full and synthetic model for Asset-Liability Management in life insurance, and analysis of the SCR with the standard formula," Papers 1908.00811,
  • Handle: RePEc:arx:papers:1908.00811

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    1. Berdin, Elia & Pancaro, Cosimo & Kok Sørensen, Christoffer, 2016. "A stochastic forward-looking model to assess the profitability and solvency of European insurers," SAFE Working Paper Series 137, Leibniz Institute for Financial Research SAFE.
    2. Fabrice Borel-Mathurin & Pierre-Emmanuel Darpeix & Quentin Guibert & Stéphane Loisel, 2018. "Main Determinants of Profit-Sharing Policy in the French Life Insurance Industry," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 43(3), pages 420-455, July.
    3. Nicole El Karoui & Stéphane Loisel & Jean-Luc Prigent & Julien Vedani, 2017. "Market inconsistencies of the market-consistent European life insurance economic valuations: pitfalls and practical solutions," Post-Print hal-01242023, HAL.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    5. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    6. Gerstner, Thomas & Griebel, Michael & Holtz, Markus & Goschnick, Ralf & Haep, Marcus, 2008. "A general asset-liability management model for the efficient simulation of portfolios of life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 704-716, April.
    7. Alexander Braun & Hato Schmeiser & Florian Schreiber, 2015. "Solvency II's Market Risk Standard Formula: How Credible Is the Proclaimed Ruin Probability," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 38(1), pages 1-30.
    8. repec:cup:astinb:v:49:y:2019:i:02:p:299-333_00 is not listed on IDEAS
    9. Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 275-297, November.
    10. Marcello Pericoli, 2018. "Macroeconomics determinants of the correlation between stocks and bonds," Temi di discussione (Economic working papers) 1198, Bank of Italy, Economic Research and International Relations Area.
    11. Floryszczak, Anthony & Le Courtois, Olivier & Majri, Mohamed, 2016. "Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a least-squares Monte-Carlo approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 15-26.
    12. 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.
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