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Valuation and hedging of the ruin-contingent life annuity (RCLA)

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  • Huaxiong Huang
  • Moshe A. Milevsky
  • Thomas S. Salisbury
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    Abstract

    This paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income per year for life, akin to a defined benefit pension, but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters. The motivation for studying the RCLA on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately \$1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. Second, the U.S. administration - both Treasury and Department of Labor - have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job.

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    File URL: http://arxiv.org/pdf/1205.3686
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1205.3686.

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    Date of creation: May 2012
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    Handle: RePEc:arx:papers:1205.3686

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    References

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    1. Geoffrey Kingston & Susan Thorp, 2004. "Annuitization and Asset Allocation with HARA Utlity," Econometric Society 2004 Australasian Meetings 248, Econometric Society.
    2. Huang, H. & Milevsky, M. A. & Wang, J., 2004. "Ruined moments in your life: how good are the approximations?," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 421-447, June.
    3. Roman N. Schulze & Thomas Post, 2010. "Individual Annuity Demand Under Aggregate Mortality Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 423-449.
    4. Griselda Deelstra & Michèle Vanmaele & David Vyncke, 2010. "Minimizing the Risk of a Financial Product Using a Put Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(4), pages 767-800.
    5. Albrecht, Peter & Maurer, Raimond, 2001. "Self-Annuitization, Ruin Risk in Retirement and Asset Allocation: The Annuity Benchmark," Sonderforschungsbereich 504 Publications 01-35, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
    6. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
    7. Milevsky,Moshe A., 2006. "The Calculus of Retirement Income," Cambridge Books, Cambridge University Press, number 9780521842587.
    8. Paul Dawson & Kevin Dowd & Andrew J. G. Cairns & David Blake, 2010. "Survivor Derivatives: A Consistent Pricing Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 579-596.
    9. Jason S. Scott & John G. Watson & Wei‐Yin Hu, 2011. "What Makes a Better Annuity?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(1), pages 213-244, 03.
    10. Albrecht, Peter & Maurer, Raimond, 2002. "Self-Annuitization, Consumption Shortfall in Retirement and Asset Allocation: The Annuity Benchmark," Journal of Pension Economics and Finance, Cambridge University Press, vol. 1(03), pages 269-288, November.
    11. Joelle H. Y. Fong & Olivia S. Mitchell & Benedict S. K. Koh, 2011. "Longevity Risk Management in Singapore's National Pension System," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(4), pages 961-982, December.
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    Cited by:
    1. Farzad Fard & Ning Rong, 2014. "Pricing and managing risks of ruin contingent life annuities under regime switching variance gamma process," Annals of Finance, Springer, vol. 10(2), pages 315-332, May.

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