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Risk comparison of different bonus distribution approaches in participating life insurance

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  • Zemp, Alexandra
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    Abstract

    The fair pricing of explicit and implicit options in life insurance products has received broad attention in the academic literature over the past years. Participating life insurance (PLI) contracts have been the focus especially. These policies are typically characterized by a term life insurance, a minimum interest rate guarantee, and bonus participation rules with regard to the insurer's asset returns or reserve situation. Researchers replicate these bonus policies quite differently. We categorize and formally present the most common PLI bonus distribution mechanisms. These bonus models closely mirror the Danish, German, British, and Italian regulatory framework. Subsequently, we perform a comparative analysis of the different bonus models with regard to risk valuation. We calibrate contract parameters so that the compared contracts have a net present value of zero and the same safety level as the initial position, using risk-neutral valuation. Subsequently, we analyze the effect of changes in the asset volatility and in the initial reserve amount (per contract) on the value of the default put option (DPO), while keeping all other parameters constant. Our results show that DPO values obtained with the PLI bonus distribution model of Bacinello (2001), which replicates the Italian regulatory framework, are most sensitive to changes in volatility and initial reserves.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 49 (2011)
    Issue (Month): 2 (September)
    Pages: 249-264

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    Handle: RePEc:eee:insuma:v:49:y:2011:i:2:p:249-264

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Participating life insurance contracts Policies with profits Interest rate guarantees;

    References

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    1. 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, Elsevier, vol. 40(1), pages 164-178, January.
    2. Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(2), pages 173-196, October.
    3. Grosen, Anders & Jensen, Bjarke & Løchte Jørgensen, Peter, 2001. "A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities," Finance Working Papers, University of Aarhus, Aarhus School of Business, Department of Business Studies 01-5, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    4. Bauer, Daniel & Kiesel, Rudiger & Kling, Alexander & Ru[ss], Jochen, 2006. "Risk-neutral valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 39(2), pages 171-183, October.
    5. 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, Elsevier, vol. 26(1), pages 37-57, February.
    6. Nadine Gatzert & Alexander Kling, 2007. "Analysis of Participating Life Insurance Contracts: A Unification Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 74(3), pages 547-570.
    7. Zaglauer, Katharina & Bauer, Daniel, 2008. "Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 43(1), pages 29-40, August.
    8. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(3), pages 533-552, December.
    9. David Prieul & Vladislav Putyatin & Tarek Nassar, 2001. "On pricing and reserving with-profits life insurance contracts," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(3), pages 145-166.
    10. Gerstner, Thomas & Griebel, Michael & Holtz, Markus & Goschnick, Ralf & Haep, Marcus, 2008. "A general asset-liability management model for the efficient simulation of portfolios of life insurance policies," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(2), pages 704-716, April.
    11. 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, Elsevier, vol. 42(2), pages 839-849, April.
    12. Tanskanen, Antti Juho & Lukkarinen, Jani, 2003. "Fair valuation of path-dependent participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 33(3), pages 595-609, December.
    13. Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(2), pages 297-323, October.
    14. Kleinow, Torsten & Willder, Mark, 2007. "The effect of management discretion on hedging and fair valuation of participating policies with maturity guarantees," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 40(3), pages 445-458, May.
    15. Kleinow, Torsten, 2009. "Valuation and hedging of participating life-insurance policies under management discretion," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 44(1), pages 78-87, February.
    16. 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, The American Risk and Insurance Association, vol. 70(3), pages 461-487.
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    Cited by:
    1. Goecke, Oskar, 2013. "Pension saving schemes with return smoothing mechanism," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 53(3), pages 678-689.
    2. 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, Elsevier, vol. 53(3), pages 491-503.
    3. 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, Elsevier, vol. 50(1), pages 64-78.

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