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Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach

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  • Fard, Farzad Alavi
  • Siu, Tak Kuen
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    Abstract

    We propose a model for the valuation of participating life insurance products under a generalized jump–diffusion model with a Markov-switching compensator. The Esscher transform is employed to determine an equivalent martingale measure in the incomplete market. The results are further manipulated through the utilization of the change of numeraire technique to reduce the dimensions of the pricing formulation. This paper is the first that extends the technique for a generalized jump–diffusion process with a Markov-switching kernel-biased completely random measure, which nests a number of important and popular models in finance. A numerical analysis is conducted to illustrate the practical implications.

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    Bibliographic Info

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

    Volume (Year): 53 (2013)
    Issue (Month): 3 ()
    Pages: 712-721

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    Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:712-721

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

    Related research

    Keywords: Participating products; Generalized jump–diffusion model; Markov-switching compensator; Esscher transform; Reduction of dimensionality; Collocation method;

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    References

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    1. 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., World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 517-532.
    2. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, Springer, vol. 1(4), pages 423-432, October.
    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. Davis, Mark H.A. & Johansson, Martin P., 2006. "Malliavin Monte Carlo Greeks for jump diffusions," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 116(1), pages 101-129, January.
    5. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, Elsevier, vol. 1(1), pages 3-15, March.
    6. Farzad Fard & Tak Siu, 2013. "Pricing and managing risks of European-style options in a Markovian regime-switching binomial model," Annals of Finance, Springer, Springer, vol. 9(3), pages 421-438, August.
    7. Albert Lo & Chung-Sing Weng, 1989. "On a class of Bayesian nonparametric estimates: II. Hazard rate estimates," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 41(2), pages 227-245, June.
    8. Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 48(5), pages 1969-84, December.
    9. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, INFORMS, vol. 46(8), pages 1116-1136, August.
    10. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 357-84, March.
    11. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, Springer, vol. 5(2), pages 201-236.
    12. A. -M. Matache & P. -A. Nitsche & C. Schwab, 2005. "Wavelet Galerkin pricing of American options on Levy driven assets," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 5(4), pages 403-424.
    13. 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.
    14. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, INFORMS, vol. 42(2), pages 269-285, February.
    15. 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.
    16. 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.
    17. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(1), pages 39-52.
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