A hierarchical credibility approach to modelling mortality rates for multiple populations

A hierarchical credibility model is a generalization of the Bühlmann credibility model and the Bühlmann-Straub credibility model with a tree structure of four or more levels. This project aims to incorporate the hierarchical credibility theory, which is used in property and casualty insurance, to model the dependency of multi-population mortality rates. The forecasting performances of the three/four/five-level hierarchical credibility models are compared with those of the classical Lee-Carter model and its three extensions for multiple populations (joint-k, cointegrated and augmented common factor Lee-Carter models). Numerical illustrations based on mortality data for both genders of the US, the UK and Japan with a series of fitting year spans and three forecasting periods show that the hierarchical credibility approach contributes to more accurate forecasts measured by the AMAPE (average of mean absolute percentage errors). The proposed model is convenient to implement and can be further applied to projecting a mortality index for pricing mortality-indexed securities.