Measuring the effect of mortality improvements on the cost of annuities

This paper uses the mortality projection model of Sithole, Haberman and Verrall [Sithole, T.Z., Haberman, S., Verrall, R.J., 2000. An investigation into parametric models for mortality projections, with applications to immediate annuitants’ and life office pensioners’ data. Insurance: Math. Econom., 27, 285–312] in order to investigate the effect of mortality improvements on the cost of annuities. Analytical results are derived using an approach which extends that of Pollard [Pollard, J.H., 1982. The expectation of life and its relationship to mortality. J. Inst. Actuar., 109, 225–240]. The results are illustrated using UK data from the Continuous Mortality Investigation Bureau. Simulation methods are used to consider the distribution of the annuity cost, as well as the more often quoted point estimates. The effects of the age of the pensioner at inception, the rate of interest and the gender of the pensioner are considered. Finally, a Bayesian model is developed which incorporates the estimation of the parameters of the mortality projection model with the simulation of the annuity cost. This allows us to consider the effect of parameter uncertainty on the projected distribution of the annuity cost.