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Analysis of Participating Life Insurance Contracts: A Unification Approach

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  • Nadine Gatzert
  • Alexander Kling

Abstract

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.

Suggested Citation

  • Nadine Gatzert & Alexander Kling, 2007. "Analysis of Participating Life Insurance Contracts: A Unification Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(3), pages 547-570, September.
    • Handle: RePEc:bla:jrinsu:v:74:y:2007:i:3:p:547-570
    DOI: 10.1111/j.1539-6975.2007.00224.x
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    Cited by:

    1. Lin, Hongcan & Saunders, David & Weng, Chengguo, 2017. "Optimal investment strategies for participating contracts," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 137-155.
    2. Andreas Reuß & Jochen Ruß & Jochen Wieland, 2016. "Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests," Risks, MDPI, vol. 4(2), pages 1-18, May.
    3. Eckert, Johanna & Gatzert, Nadine & Martin, Michael, 2016. "Valuation and risk assessment of participating life insurance in the presence of credit risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 382-393.
    4. Ninna Reitzel Jensen & Kristian Juul Schomacker, 2015. "A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk," Risks, MDPI, vol. 3(2), pages 1-36, June.
    5. Berdin, Elia, 2016. "Interest rate risk, longevity risk and the solvency of life insurers," ICIR Working Paper Series 23/16, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    6. Bruszas, Sandy & Kaschützke, Barbara & Maurer, Raimond & Siegelin, Ivonne, 2018. "Unisex pricing of German participating life annuities—Boon or bane for customer and insurance company?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 230-245.
    7. Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Papers 0908.3196, arXiv.org.
    8. Felix Fie{ss}inger & Mitja Stadje, 2024. "Mean-Variance Optimization for Participating Life Insurance Contracts," Papers 2407.11761, arXiv.org, revised Dec 2024.
    9. Gatzert, Nadine, 2008. "Asset management and surplus distribution strategies in life insurance: An examination with respect to risk pricing and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 839-849, April.
    10. Eling, Martin & Holder, Stefan, 2013. "The value of interest rate guarantees in participating life insurance contracts: Status quo and alternative product design," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 491-503.
    11. Chen, An & Stadje, Mitja & Zhang, Fangyuan, 2024. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 114-129.
    12. Zemp, Alexandra, 2011. "Risk comparison of different bonus distribution approaches in participating life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 249-264, September.
    13. Graf, Stefan & Kling, Alexander & Ruß, Jochen, 2011. "Risk analysis and valuation of life insurance contracts: Combining actuarial and financial approaches," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 115-125, July.
    14. Bernard Carole & Le Courtois Olivier, 2012. "Asset Risk Management of Participating Contracts," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(2), pages 1-23, June.
    15. Lin, Jyh-Horng & Li, Xuelian, 2017. "Regulatory policies on Gramm-Leach-Bliley consolidation of commercial banking, shadow banking, and life insurance," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 50(C), pages 69-84.
    16. Bohnert, Alexander & Gatzert, Nadine, 2012. "Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 64-78.
    17. Antje Mahayni & Matthias Muck, 2017. "The benefit of life insurance contracts with capped index participation when stock prices are subject to jump risk," Review of Derivatives Research, Springer, vol. 20(3), pages 281-308, October.
    18. Alexander Bohnert, 2015. "The Impact of Guarantees on the Performance of Pension Saving Schemes: Insights from the Literature," Risks, MDPI, vol. 3(4), pages 1-28, November.
    19. Lukasz Delong, 2010. "Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management," Papers 1005.4417, arXiv.org, revised Jan 2011.
    20. Hainaut, Donatien & Devineau, Laurent, 2024. "Participating life insurances in an equity-Libor Market Model," LIDAM Discussion Papers ISBA 2024015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    21. Bohnert, Alexander & Gatzert, Nadine & Jørgensen, Peter Løchte, 2015. "On the management of life insurance company risk by strategic choice of product mix, investment strategy and surplus appropriation schemes," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 83-97.
    22. Martin Eling & Dieter Kiesenbauer, 2012. "Does Surplus Participation Reflect Market Discipline? An Analysis of the German Life Insurance Market," Journal of Financial Services Research, Springer;Western Finance Association, vol. 42(3), pages 159-185, December.
    23. Gatzert, Nadine, 2019. "An analysis of transaction costs in participating life insurance under mean–variance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 185-197.

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