A Computationally Efficient Algorithm for Estimating the Distribution of Future Annuity Values Under Interest-Rate and Longevity Risks |
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| Authors: | Kevin Dowd PhD David Blake PhD Andrew J G Cairns PhD |
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| Institution: | 1. Pensions Institute, Cass Business School , 106 Bunhill Row, London EC1Y 8TZ , UK;2. Economics and Director of the Pensions Institute at Cass Business School , 106 Bunhill Row, London EC1Y 8TZ , UK;3. Financial Mathematics, Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences , Heriot-Watt University , Edinburgh EH14 4AS , United Kingdom |
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| Abstract: | 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. |
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