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A Computationally Efficient Algorithm for Estimating the Distribution of Future Annuity Values Under Interest-Rate and Longevity Risks

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  • Kevin Dowd
  • David Blake
  • Andrew Cairns

Abstract

This paper proposes a computationally efficient algorithm for quantifying the impact of interestrate risk and longevity risk on the distribution of annuity values in the distant future. The algorithm simulates the state variables out to the end of the horizon period and then uses a Taylor series approximation to compute approximate annuity values at the end of that period, thereby avoiding a computationally expensive “simulation-within-simulation” problem. Illustrative results suggest that annuity values are likely to rise considerably but are also quite uncertain. These findings have some unpleasant implications both for defined contribution pension plans and for defined benefit plan sponsors considering using annuities to hedge their exposure to these risks at some point in the future.

Suggested Citation

  • Kevin Dowd & David Blake & Andrew Cairns, 2011. "A Computationally Efficient Algorithm for Estimating the Distribution of Future Annuity Values Under Interest-Rate and Longevity Risks," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 237-247.
    • Handle: RePEc:taf:uaajxx:v:15:y:2011:i:2:p:237-247
    DOI: 10.1080/10920277.2011.10597619
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    Cited by:

    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    3. David Blake & Christophe Courbage & Richard MacMinn & Michael Sherris, 2011. "Longevity Risk and Capital Markets: The 2010–2011 Update," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(4), pages 489-500, October.
    4. Andreas Niemeyer, 2015. "Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework," Risks, MDPI, vol. 3(1), pages 1-26, January.
    5. Srichander Ramaswamy, 2012. "The sustainability of pension schemes," BIS Working Papers 368, Bank for International Settlements.
    6. Feng, Ben Mingbin & Li, Johnny Siu-Hang & Zhou, Kenneth Q., 2022. "Green nested simulation via likelihood ratio: Applications to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 285-301.

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