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Valuing Guaranteed Minimum Death Benefit Options in Variable Annuities Under a Benchmark Approach

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Variable annuities (VAs) represent a marked change from earlier life products in the guarantees that they offer and it is no longer possible to manage the risks of these liabilities using traditional actuarial methods. Thinking about guarantees as options suggests applying risk neutral pricing in order to value the embedded guarantees, such as guaranteed minimum death benefits (GMDBs). However, due to the long maturities of contracts, stochastic volatility and many other reasons, VA markets are incomplete. In this paper we propose a methodology for pricing GMDBs under a benchmark approach which does not require the existence of a risk neutral probability measure. We assume that the insurance company invests in the growth optimal portfolio of its investment universe and apply real world pricing rather than risk neutral pricing. In particular, we consider the minimal market model and conclude that in this setup the fair price of a roll-up GMDB is lower than the price obtained by applying standard risk neutral pricing. Moreover, we take into account rational as well as irrational lapsation of the policyholder.

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  • T. Marquardt & Eckhard Platen & S. Jaschke, 2008. "Valuing Guaranteed Minimum Death Benefit Options in Variable Annuities Under a Benchmark Approach," Research Paper Series 221, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:221
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp221.pdf
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    1. Bühlmann, Hans & Platen, Eckhard, 2003. "A Discrete Time Benchmark Approach for Insurance and Finance," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 153-172, November.
    2. David Heath & Eckhard Platen, 2002. "Consistent pricing and hedging for a modified constant elasticity of variance model," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 459-467.
    3. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    4. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    5. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.

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    Keywords

    Benchmark approach; fair pricing; GMDB; growth optimal portfolio; lapsation; local volatility function; minimal market model; variable annuities;
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