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Fair valuation of insurance contracts under Lévy process specifications

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  • Kassberger, Stefan
  • Kiesel, Rüdiger
  • Liebmann, Thomas

Abstract

The valuation of options embedded in insurance contracts using concepts from financial mathematics (in particular, from option pricing theory), typically referred to as fair valuation, has recently attracted considerable interest in academia as well as among practitioners. The aim of this article is to investigate the valuation of participating and unit-linked life insurance contracts, which are characterized by embedded rate guarantees and bonus distribution rules. In contrast to the existing literature, our approach models the dynamics of the reference portfolio by means of an exponential Lévy process. Our analysis sheds light on the impact of the dynamics of the reference portfolio on the fair contract value for several popular types of insurance policies. Moreover, it helps to assess the potential risk arising from misspecification of the stochastic process driving the reference portfolio.

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Bibliographic Info

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

Volume (Year): 42 (2008)
Issue (Month): 1 (February)
Pages: 419-433

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Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:419-433

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

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  1. Cummins, J. David & Miltersen, Kristian R. & Persson, Svein-Arne, 2004. "International Comparison of Interest Rate Guarantees in Life Insurance," Discussion Papers 2004/18, Department of Business and Management Science, Norwegian School of Economics.
  2. 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.
  3. Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 173-196, October.
  4. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, 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, vol. 26(1), pages 37-57, February.
  6. 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, vol. 36(3), pages 499-516, June.
  7. 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, vol. 70(3), pages 461-487.
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Cited by:
  1. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
  2. Julien Chevallier & Benoît Sévi, 2012. "On the Stochastic Properties of Carbon Futures Prices," Working Papers halshs-00720166, HAL.
  3. Lee, Chien-Chiang & Huang, Wei-Ling & Yin, Chun-Hao, 2013. "The dynamic interactions among the stock, bond and insurance markets," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 28-52.

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