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Designing and pricing guarantee options in defined contribution pension plans


  • Consiglio, Andrea
  • Tumminello, Michele
  • Zenios, Stavros A.


The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. However, for DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio and we develop a discrete model that selects the reference portfolio to minimize the cost of a guarantee. While the relation DB–DC is typically viewed as a binary one, the model shows how to price a wide range of guarantees creating a continuum between DB and DC. Integrating guarantee pricing with asset allocation decision is useful to both pension fund managers and regulators. The former are given a yardstick to assess if a given asset portfolio is fit-for-purpose; the latter can assess differences of specific reference funds with respect to the optimal one, signaling possible cases of moral hazard. We develop the model and report numerical results to illustrate its uses.

Suggested Citation

  • Consiglio, Andrea & Tumminello, Michele & Zenios, Stavros A., 2015. "Designing and pricing guarantee options in defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 267-279.
  • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:267-279
    DOI: 10.1016/j.insmatheco.2015.10.002

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    References listed on IDEAS

    1. Consiglio, Andrea & Saunders, David & Zenios, Stavros A., 2006. "Asset and liability management for insurance products with minimum guarantees: The UK case," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 645-667, February.
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    5. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2010. "No-arbitrage conditions, scenario trees, and multi-asset financial optimization," European Journal of Operational Research, Elsevier, vol. 206(3), pages 609-613, November.
    6. Delia Velculescu, 2010. "Some Uncomfortable Arithmetic Regarding Europe’s Public Finances," IMF Working Papers 10/177, International Monetary Fund.
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    8. Smetters, Kent, 2002. "Controlling the cost of minimum benefit guarantees in public pension conversions," Journal of Pension Economics and Finance, Cambridge University Press, vol. 1(1), pages 9-33, March.
    9. Pablo Antolín & Stéphanie Payet & Edward Whitehouse & Juan Yermo, 2011. "The Role of Guarantees in Defined Contribution Pensions," OECD Working Papers on Finance, Insurance and Private Pensions 11, OECD Publishing.
    10. T. F. Coleman & Y. Kim & Y. Li & M. Patron, 2007. "Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 347-376, June.
    11. 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, September.
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    Cited by:

    1. Pierre Devolder & Sébastien De Valeriola, 2017. "Minimum Protection in DC Funding Pension Plans and Margrabe Options," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-14, January.


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