A step-by-step guide to building two-population stochastic mortality models

Abstract

Two-population stochastic mortality models play a crucial role in the securitization of longevity risk. In particular, they allow us to quantify the population basis risk when longevity hedges are built from broad-based mortality indexes. In this paper, we propose and illustrate a systematic process for constructing a two-population mortality model for a pair of populations. The process encompasses four steps, namely (1) determining the conditions for biological reasonableness, (2) identifying an appropriate base model specification, (3) choosing a suitable time-series process and correlation structure for projecting period and/or cohort effects into the future, and (4) model evaluation.For each of the seven single-population models from Cairns et al. (2009), we propose two-population generalizations. We derive criteria required to avoid long-term divergence problems and the likelihood functions for estimating the models. We also explain how the parameter estimates are found, and how the models are systematically simplified to optimize the fit based on the Bayes Information Criterion. Throughout the paper, the results and methodology are illustrated using real data from two pairs of populations.