A common age effect model for the mortality of multiple populations

Abstract

a b s t r a c tWe introduce a model for the mortality rates of multiple populations. To build the proposed model we investigate to what extent a common age effect can be found among the mortality experiences of several countries and use a common principal component analysis to estimate a common age effect in an age-period model for multiple populations. The fit of the proposed model is then compared to age-period models fitted to each country individually, and to the fit of the model proposed by Li and Lee (2005).Although we do not consider stochastic mortality projections in this paper, we argue that the proposed common age effect model can be extended to a stochastic mortality model for multiple populations, which allows to generate mortality scenarios simultaneously for all considered populations. This is particularly relevant when mortality derivatives are used to hedge the longevity risk in an annuity portfolio as this often means that the underlying population for the derivatives is not the same as the population in the annuity portfolio.

Multi-population mortality models: fitting, forecasting and comparisons

“…We compared the multi-population mortality model by Li and Lee (2005) and two of its variants with the Common Age Effect (CAE) model by Kleinow (2014) using mortality data from six countries. All models have identifiability problems that have been addressed by applying exact and quasi identifiability constraints.…”

“…We propose, test and compare four models: the Li and Lee model introduced by Li and Lee (2005), two variations of this model, and the common age effect model introduced by Kleinow (2014). The two variations of the Li and Lee model provide a significant reduction in the number of parameters k, which results in a considerable reduction of computing time and, also, potentially result in more robust forecasts.…”

“…However, their choice of stochastic mortality models and time series models means that forecasts are not coherent. The model Kleinow (2014) proposes -a common age effect (CAE) multi-population model, we examine in this paper more thoughtfully.…”

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AbstractWe review a number of multi-population mortality models: variations of the Li and Lee (2005) model, and the common-age-effect (CAE) model of Kleinow (2014). Model parameters are estimated using maximum likelihood.

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A Comparative Study of Two-Population Models for the Assessment of Basis Risk in Longevity Hedges

“…For modelling the period indexes κ 1 t and κ 2 t , Zhou et al (2014) consider three methods: a random walk with drift for κ 1 t plus an AR(1) for κ 2 t − κ 1 t (abbreviated RWAR by the authors), a vector autoregressive model (VAR); and a Vector Error Correction Model (VECM). Similarly to Zhou et al (2014), Kleinow (2015) has proposed a multiple population Common-Age-Effect model in which the age-sensitivity terms (age-effects) are common to all the populations. Another alternative for modelling multi-population mortality is to extend the widely used single-population Cairns-Blake-Dowd (CBD) model of mortality (Cairns et al, 2006).…”