Modeling Longevity Risk using Extreme Value Theory: An Empirical Investigation using Portuguese and Spanish Population Data

Abstract

Extreme value theory (EVT) provides a framework to formalize the study of behaviour in the tails of a distribution. In this paper we use EVT to model the statistical behaviour of mortality rates over a given high threshold age and to estimate the significance of rare longevity risk in a given population. We adopt a piecewise approach in estimating the optimal threshold age using an iterative algorithm of maximum likelihood estimation.that statistically determines the cut-off between the central (Gompertz) part of the distribution and the upper tail modelled using the generalized Pareto distribution. The model is empirically tested using the most recent period mortality data for the total, male and female populations of Portugal and Spain. We use some classical results from EVT to estimate the evolution of the theoretical maximum life span over time and to derive confidence intervals for the central estimates. We then use time series methods to forecast the highest attained age. We observe a good fit of the model in all populations and subperiods analysed and on the whole life span considered. We estimate an increase in the theoretical maximum life span over time for all populations, more significant in the male subpopulations.