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Pricing Participating Policies With Rate Guarantees

Author

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  • CHI CHIU CHU

    (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • YUE KUEN KWOK

    (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

Abstract

We construct the contingent claims models that price participating policies with rate guarantees and default risk. These policies are characterized by the sharing of profits from an investment portfolio between the insurer and the policyholders. A certain reserve distribution mechanism is employed to credit interest at or above certain specified guaranteed rate periodically to the policyholders. Besides the reversionary reserve distribution, terminal bonus is also paid to the policyholders if the terminal surplus is positive. However, the insurer may default at maturity and the policyholders can only receive the residual assets. By neglecting market frictions, mortality risk and surrender option, and under certain assumptions on the interest rate crediting mechanism, we are able to find analytic approximation solution to the pricing model using perturbation techniques. We also develop effective finite difference algorithms for the numerical solution of the contingent claims models. Pricing behaviors of these participating policies with respect to various parameters in the pricing models are examined.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:04:n:s0219024906003688
    DOI: 10.1142/S0219024906003688
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    References listed on IDEAS

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    1. Consiglio, Andrea & Cocco, Flavio & Zenios, Stavros A., 2008. "Asset and liability modelling for participating policies with guarantees," European Journal of Operational Research, Elsevier, vol. 186(1), pages 380-404, April.
    2. Laura Ballotta & Steven Haberman & Nan Wang, 2006. "Guarantees in With‐Profit and Unitized With‐Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 97-121, March.
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    Cited by:

    1. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    2. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Maria B. Chiarolla & Tiziano Angelis & Gabriele Stabile, 2022. "An analytical study of participating policies with minimum rate guarantee and surrender option," Finance and Stochastics, Springer, vol. 26(2), pages 173-216, April.
    4. 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.

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