**DISCUSSION PAPER PI-0823**

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
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.