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Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option

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  • Anna Rita Bacinello
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    Abstract

    In this article we deal with the problem of pricing a guaranteed life insurance participating policy, sold in the Italian market, which embeds a surrender option. This feature is an American-style put option that enables the policyholder to sell back the contract to the insurer at the cash surrender value. Employing a recursive binomial formula patterned after the Cox, Ross, and Rubinstein (1979) discrete option pricing model we compute, first of all, the total price of the contract, which also includes a compensation for the participation feature ("participation option," henceforth). Then this price is split into the value of three components: the "basic contract", the "participation option", and the "surrender option". The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice. Copyright The Journal of Risk and Insurance.

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    Bibliographic Info

    Article provided by The American Risk and Insurance Association in its journal The Journal of Risk and Insurance.

    Volume (Year): 70 (2003)
    Issue (Month): 3 ()
    Pages: 461-487

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    Handle: RePEc:bla:jrinsu:v:70:y:2003:i:3:p:461-487

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    Cited by:
    1. Eling, Martin & Holder, Stefan, 2012. "The Value of Interest Rate Guarantees in Participating Life insurance Contracts: Status Quo and Alternative Product Design," Working Papers on Finance 1221, University of St. Gallen, School of Finance.
    2. Bernard, Carole & MacKay, Anne & Muehlbeyer, Max, 2014. "Optimal surrender policy for variable annuity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 116-128.
    3. Lin, Shih-Kuei & Lin, Chien-Hsiu & Chuang, Ming-Che & Chou, Chia-Yu, 2014. "A recursive formula for a participating contract embedding a surrender option under regime-switching model with jump risks: Evidence from stock indices," Economic Modelling, Elsevier, vol. 38(C), pages 341-350.
    4. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    5. 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.
    6. 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.
    7. Su, Karen C., 2010. "The conversion option in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 437-442, June.
    8. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer, vol. 14(3), pages 255-275, September.
    9. Bohnert, Alexander & Gatzert, Nadine, 2012. "Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 64-78.
    10. Kling, Alexander & Richter, Andreas & Ru[ss], Jochen, 2007. "The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 164-178, January.
    11. Kassberger, Stefan & Kiesel, Rüdiger & Liebmann, Thomas, 2008. "Fair valuation of insurance contracts under Lévy process specifications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 419-433, February.
    12. Bacinello, Anna Rita, 2005. "Endogenous model of surrender conditions in equity-linked life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 270-296, October.
    13. 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.
    14. Consiglio, Andrea & De Giovanni, Domenico, 2008. "Evaluation of insurance products with guarantee in incomplete markets," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 332-342, February.
    15. 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.
    16. Kling, Alexander & Richter, Andreas & Ruß, Jochen, 2006. "The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees," Discussion Papers in Business Administration 1220, University of Munich, Munich School of Management.
    17. Kochanski, Michael, 2010. "Solvency capital requirement for German unit-linked insurance products," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 6(2), pages 33-70.
    18. Gatzert, Nadine, 2008. "Asset management and surplus distribution strategies in life insurance: An examination with respect to risk pricing and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 839-849, April.
    19. Goecke, Oskar, 2013. "Pension saving schemes with return smoothing mechanism," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 678-689.
    20. Bauer, Daniel & Kiesel, Rudiger & Kling, Alexander & Ru[ss], Jochen, 2006. "Risk-neutral valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 171-183, October.
    21. De Giovanni, Domenico, 2007. "Lapse Rate Modeling: A Rational Expectation Approach," Finance Research Group Working Papers F-2007-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    22. Martin Eling & Michael Kochanski, 2013. "Research on lapse in life insurance: what has been done and what needs to be done?," Journal of Risk Finance, Emerald Group Publishing, vol. 14(4), pages 392-413, July.

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