A note on pricing inflation-indexed life annuities

This paper deals with the topic of inflation protection of pensions and the pricing process for inflation-indexed life annuities. Several ways of partial indexation of pensions are taken into consideration. Future inflation paths are obtained by simulation of a stochastic time series model. The main advantage of the proposed methodology is that it allows the pricing of partially inflation-indexed pensions. The pricing process is based on the hypothesis that the annuities provider guarantees a certain level of the real interest rate. Certain numerical results are obtained. Taking into account that inflation is generated by autoregressive processes of order one AR(1), empirical distributions of the expected present value (EPV) are determined for some partial inflation-indexed life annuities. Numerical results achieved for an AR(1) model that describes the evolution of the inflation rate in Spain during the period 1962-2005 are also presented. Results gained allow the comparison of the mean and standard deviation calculated on the basis of empirical distributions of the EPV for various types of partially indexed annuities, and also for various values of AR(1) model parameters. By flexible offers, insurers may meet the expectations of the annuitants, regarding both price and guaranteed protection against inflation.