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The Effect of Secondary Markets on Equity-Linked Life Insurance with Surrender Guarantees

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  • Hilpert, Christian
  • Li, Jing
  • Szimayer, Alexander

Abstract

We study the effect of secondary markets on equity-linked life insurance contracts with surrender guarantees. The policyholders are assumed to be boundedly rational in giving up their contracts, and a proportion of policyholders will access the secondary markets instead of surrendering the contracts to the insurance company. We formulate the valuation problems from both the insurance company's and the policyholders' perspectives and characterize the contract values by deriving the respective pricing PDEs. Comparative statics are derived indicating the effect of the level of the policyholder's rationality and secondary market characteristics such as accessibility and competition on the contract values. The pricing PDEs are solved numerically via the Crank-Nicolson scheme to study the implication of the inclusion of a secondary market. We show that a secondary market generally increases the risk borne by the insurance company and the policyholders profit from the secondary market only when the secondary market is sufficiently competitive. Furthermore, we derive the necessary condition for the existence of a fair contract in this context and study the effect of the secondary market on fair contract design.

Suggested Citation

  • Hilpert, Christian & Li, Jing & Szimayer, Alexander, 2011. "The Effect of Secondary Markets on Equity-Linked Life Insurance with Surrender Guarantees," Bonn Econ Discussion Papers 11/2011, University of Bonn, Bonn Graduate School of Economics (BGSE).
    • Handle: RePEc:zbw:bonedp:112011
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    References listed on IDEAS

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    1. Nadine Gatzert & Gudrun Hoermann & Hato Schmeiser, 2009. "The Impact of the Secondary Market on Life Insurers’ Surrender Profits," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 887-908, December.
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    Cited by:

    1. Anne MacKay & Maciej Augustyniak & Carole Bernard & Mary R. Hardy, 2017. "Risk Management of Policyholder Behavior in Equity-Linked Life Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 661-690, June.
    2. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework," Risks, MDPI, vol. 4(3), pages 1-31, July.
    3. Cheng, Chunli & Hilpert, Christian & Miri Lavasani, Aidin & Schaefer, Mick, 2023. "Surrender contagion in life insurance," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1465-1479.
    4. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.
    5. Lu Yu & Jiang Cheng & Tzuting Lin, 2019. "Life insurance lapse behaviour: evidence from China," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(4), pages 653-678, October.

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    More about this item

    Keywords

    equity-linked life insurance contracts; surrender guarantee; bounded rationality; fair contract analysis; secondary market;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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