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On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View

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  • Bauer, Daniel
  • Bergmann, Daniela
  • Kiesel, Rüdiger

Abstract

In recent years, market-consistent valuation approaches have gained an increasing importance for insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published. In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems. Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their efficiency in a simple and a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the influence of model risk by additionally introducing an exponential Lévy model.

Suggested Citation

  • Bauer, Daniel & Bergmann, Daniela & Kiesel, Rüdiger, 2010. "On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 65-95, May.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:01:p:65-95_00
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    Cited by:

    1. 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.
    2. Jan Natolski & Ralf Werner, 2017. "Mathematical Analysis of Replication by Cash Flow Matching," Risks, MDPI, vol. 5(1), pages 1-15, February.
    3. Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. "Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed Benefits with Dynamic Policyholder Behavior," Tinbergen Institute Discussion Papers 15-008/IV/DSF85, Tinbergen Institute.
    4. Hainaut, Donatien, 2012. "Multidimensional Lee–Carter model with switching mortality processes," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 236-246.
    5. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    6. Schmeiser, H. & Wagner, J., 2011. "A joint valuation of premium payment and surrender options in participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 580-596.
    7. Cheng, Chunli & Li, Jing, 2018. "Early default risk and surrender risk: Impacts on participating life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 30-43.
    8. Mathieu Cambou & Damir Filipović, 2018. "Replicating portfolio approach to capital calculation," Finance and Stochastics, Springer, vol. 22(1), pages 181-203, January.
    9. Anna Rita Bacinello & An Chen & Thorsten Sehner & Pietro Millossovich, 2021. "On the Market-Consistent Valuation of Participating Life Insurance Heterogeneous Contracts under Longevity Risk," Risks, MDPI, vol. 9(1), pages 1-18, January.

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