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An analytical study of participating policies with minimum rate guarantee and surrender option

Author

Listed:
  • Maria B. Chiarolla
  • Tiziano De Angelis
  • Gabriele Stabile

Abstract

We perform a detailed theoretical study of the value of a class of participating policies with four key features: $(i)$ the policyholder is guaranteed a minimum interest rate on the policy reserve; $(ii)$ the contract can be terminated by the holder at any time until maturity (surrender option); $(iii)$ at the maturity (or upon surrender) a bonus can be credited to the holder if the portfolio backing the policy outperforms the current policy reserve; $(iv)$ due to solvency requirements the contract ends if the value of the underlying portfolio of assets falls below the policy reserve. Our analysis is probabilistic and it relies on optimal stopping and free boundary theory. We find a structure of the optimal surrender strategy which was undetected by previous (mostly numerical) studies on the same topic. Optimal surrender of the contract is triggered by two `stop-loss' boundaries and by a `too-good-to-persist' boundary (in the language of \cite{EV20}). Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments.

Suggested Citation

  • Maria B. Chiarolla & Tiziano De Angelis & Gabriele Stabile, 2020. "An analytical study of participating policies with minimum rate guarantee and surrender option," Papers 2004.06982, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2004.06982
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    References listed on IDEAS

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    1. 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.
    2. Chi Chiu Chu & Yue Kuen Kwok, 2006. "Pricing Participating Policies With Rate Guarantees," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 517-532.
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    4. Anna Rita Bacinello, 2003. "Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(3), pages 461-487, September.
    5. Gabriele Stabile, 2006. "Optimal Timing Of The Annuity Purchase: Combined Stochastic Control And Optimal Stopping Problem," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 151-170.
    6. Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
    7. Tiziano De Angelis & Yerkin Kitapbayev, 2018. "On the Optimal Exercise Boundaries of Swing Put Options," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 252-274, February.
    8. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
    9. Tiziano Angelis & Gabriele Stabile, 2019. "On the free boundary of an annuity purchase," Finance and Stochastics, Springer, vol. 23(1), pages 97-137, January.
    10. Nolte, Sven & Schneider, Judith C., 2017. "Don’t lapse into temptation: a behavioral explanation for policy surrender," Journal of Banking & Finance, Elsevier, vol. 79(C), pages 12-27.
    11. Ekström, Erik & Vaicenavicius, Juozas, 2020. "Optimal stopping of a Brownian bridge with an unknown pinning point," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 806-823.
    12. 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.
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    Cited by:

    1. Anne Mackay & Marie-Claude Vachon, 2023. "On an Optimal Stopping Problem with a Discontinuous Reward," Papers 2311.03538, arXiv.org, revised Nov 2023.
    2. Tiziano De Angelis, 2020. "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon," Papers 2009.01276, arXiv.org, revised Jan 2022.

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    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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