Selecting stochastic mortality models for the Italian population

Abstract

The future revision of capital requirements and a market-consistent valuation of non-hedgeable liabilities lead to an increasing attention on forecasting longevity trends. In this field, many methodologies focus on either modeling mortality or pricing mortality-linked securities (as longevity bonds). Following Lee–Carter method (proposed in 1992), actuarial literature has provided several extensions in order to consider different trends observed in European data set (e.g., the cohort effect). The purpose of the paper is to compare the features of main mortality models proposed over the years. Model selection became indeed a primary task with the aim to identify the “best” model. What is meant by best is controversial, but good selection techniques are usually based on a good balance between goodness of fit and simplicity. In this regard, different criteria, mainly based on residual and projected rates analysis, are here used. For the sake of comparison, main forecasting methods have been applied to deaths and exposures to risk of male Italian population. Weaknesses and strengths have been emphasized, by underlying how various models provide a different goodness of fit according to different data sets. At the same time, the quality and the variability of forecasted rates have been compared by evaluating the effect on annuity values. Results confirm that some models perform better than others, but no single model can be defined as the best method.