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

Kevin Dowd, David Blake and Andrew J.G. Cairns

This paper proposes a computationally efficient algorithm for quantifying the impact of interest-rate 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 for both 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.

JEL Classification Numbers: G23, C15, C53

Key words: longevity risk, interest-rate risk, annuity values, Taylor series approximation, pension risk

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