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Optimal design of profit sharing rates by FFT

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  • Hainaut, Donatien

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.

Suggested Citation

  • Hainaut, Donatien, 2010. "Optimal design of profit sharing rates by FFT," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 470-478, June.
  • Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:470-478
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    References listed on IDEAS

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    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, vol. 26(1), pages 37-57, February.
    6. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    7. Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 31(02), pages 275-297, November.
    8. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
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