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Regret aversion and annuity risk in defined contribution pension plans

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  • Frehen, Rik G.P.
  • Hoevenaars, Roy P.M.M.
  • Palm, Franz C.
  • Schotman, Peter C.

Abstract

The high value of the implicit option to choose a retirement date at which interest rates are particularly high and life annuities relatively cheap, leads to the possibility to introduce regret aversion in the retirement investment decision of defined contribution plan participants. As a remedy for regret aversion in retirement investment decisions, this paper develops and prices a lookback option on a life annuity contract. We determine a closed-form option value under the restriction that the option holder invests risklessly during the time to maturity of the option and without the guarantee that the exact amount of retirement wealth is converted into a life annuity at retirement. Thereafter the investment restriction is relaxed and the guarantee of exact conversion is imposed and the option is priced via Monte Carlo simulations in an economic environment with a stochastic discount factor. Option price sensitivities are determined via the pricing of alternative options. We find that the price of a lookback option, with a maturity of three years, amounts to 8%-9% of the wealth at the option issuance date. The option price is highly sensitive to the exercise price of the option, i.e. pricing alternative options (e.g. Asian) substantially lowers the price. Time to maturity and interest rate volatility are other important option price drivers. Asset allocation decisions and initial interest rates hardly affect the option price.

Suggested Citation

  • Frehen, Rik G.P. & Hoevenaars, Roy P.M.M. & Palm, Franz C. & Schotman, Peter C., 2008. "Regret aversion and annuity risk in defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1050-1061, June.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1050-1061
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    as
    1. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    2. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    3. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    4. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    5. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    6. John H. Cochrane & Monika Piazzesi, 2005. "Bond Risk Premia," American Economic Review, American Economic Association, vol. 95(1), pages 138-160, March.
    7. Robert C. Merton & Zvi Bodie, 2005. "Design Of Financial Systems: Towards A Synthesis Of Function And Structure," World Scientific Book Chapters, in: H Gifford Fong (ed.), The World Of Risk Management, chapter 1, pages 1-27, World Scientific Publishing Co. Pte. Ltd..
    8. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    9. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    10. Michael Braun & Alexander Muermann, 2004. "The Impact of Regret on the Demand for Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(4), pages 737-767, December.
    11. Marie‐Eve Lachance & Olivia S. Mitchell & Kent Smetters, 2003. "Guaranteeing Defined Contribution Pensions: The Option to Buy Back a Defined Benefit Promise," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(1), pages 1-16, March.
    12. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    13. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, January.
    14. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
    15. Muermann, Alexander & Mitchell, Olivia S. & Volkman, Jacqueline M., 2006. "Regret, portfolio choice, and guarantees in defined contribution schemes," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 219-229, October.
    16. Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
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    Cited by:

    1. Michael Nwogugu, 2020. "Regret Theory And Asset Pricing Anomalies In Incomplete Markets With Dynamic Un-Aggregated Preferences," Papers 2005.01709, arXiv.org.

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