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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 & 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 defined contribution
pension plans.

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