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Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

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  • Zaglauer, Katharina
  • Bauer, Daniel

Abstract

Over the last years, the valuation of life insurance contracts using concepts from financial mathematics has become a popular research area for actuaries as well as financial economists. In particular, several methods have been proposed of how to model and price participating policies, which are characterized by an annual interest rate guarantee and some bonus distribution rules. However, despite the long terms of life insurance products, most valuation models allowing for sophisticated bonus distribution rules and the inclusion of frequently offered options assume a simple Black-Scholes setup and, more specifically, deterministic or even constant interest rates. We present a framework in which participating life insurance contracts including predominant kinds of guarantees and options can be valuated and analyzed in a stochastic interest rate environment. In particular, the different option elements can be priced and analyzed separately. We use Monte Carlo and discretization methods to derive the respective values. The sensitivity of the contract and guarantee values with respect to multiple parameters is studied using the bonus distribution schemes as introduced in [Bauer, D., Kiesel, R., Kling, A., Ruß, J., 2006. Risk-neutral valuation of participating life insurance contracts. Insurance: Math. Econom. 39, 171-183]. Surprisingly, even though the value of the contract as a whole is only moderately affected by the stochasticity of the short rate of interest, the value of the different embedded options is altered considerably in comparison to the value under constant interest rates. Furthermore, using a simplified asset portfolio and empirical parameter estimations, we show that the proportion of stock within the insurer's asset portfolio substantially affects the value of the contract.

Suggested Citation

  • Zaglauer, Katharina & Bauer, Daniel, 2008. "Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 29-40, August.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:29-40
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    Cited by:

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    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Maciej Augustyniak & Mathieu Boudreault, 2017. "Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 502-525, October.
    8. 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.
    9. Hieber, Peter, 2017. "Cliquet-style return guarantees in a regime switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 138-147.
    10. David Markantonis & G.-Fivos Sargentis & Panayiotis Dimitriadis & Theano Iliopoulou & Aimilia Siganou & Konstantina Moraiti & Maria Nikolinakou & Ilias Taygetos Meletopoulos & Nikos Mamassis & Demetri, 2023. "Stochastic Evaluation of the Investment Risk by the Scale of Water Infrastructures—Case Study: The Municipality of West Mani (Greece)," World, MDPI, vol. 4(1), pages 1-20, January.
    11. Jack Clark Francis & Arie Harel & Giora Harpaz, 2010. "Actuarially Fair Premia for Deductible Insurance Policies," The American Economist, Sage Publications, vol. 55(2), pages 83-91, November.
    12. Poletti Laurini, Márcio & Moura, Marcelo, 2010. "Constrained smoothing B-splines for the term structure of interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 339-350, April.

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