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Optimal design of profit sharing rates by FFT

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  • Hainaut, Donatien
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    Abstract

    This paper addresses the calculation of a fair profit sharing rate for participating policies with a minimum interest rate guaranteed. The bonus credited to policies depends on the performance of a basket of two assets: a stock and a zero coupon bond and on the guarantee. The dynamics of the instantaneous short rates are driven by a Hull and White model, whereas the stocks follow a double exponential jump-diffusion model. The participation level is determined such that the return retained by the insurer is sufficient to hedge the interest rate guaranteed. Given that the return of the total asset is not lognormal, we rely on a Fast Fourier Transform to compute the fair value of bonus and guarantee options.

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    Bibliographic Info

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

    Volume (Year): 46 (2010)
    Issue (Month): 3 (June)
    Pages: 470-478

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    Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:470-478

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

    Related research

    Keywords: Policies with profit Fast Fourier Transform Fair pricing;

    References

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    1. 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.
    2. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, Francois, 2005. "Market value of life insurance contracts under stochastic interest rates and default risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 36(3), pages 499-516, June.
    3. 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.
    4. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, INFORMS, vol. 48(8), pages 1086-1101, August.
    5. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, INFORMS, vol. 50(9), pages 1178-1192, September.
    6. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 32(02), pages 239-248, June.
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