A Square-Root Factor-Based Multi-Population Extension of the Mortality Laws

Abstract

In this paper, we present and calibrate a multi-population stochastic mortality model based on latent square-root affine factors of the Cox-Ingersoll and Ross type. The model considers a generalization of the traditional actuarial mortality laws to a stochastic, multi-population and time-varying setting. We calibrate the model to fit the mortality dynamics of UK males and females over the last 50 years. We estimate the optimal states and model parameters using quasi-maximum likelihood techniques.

Multi-population mortality modeling with Lévy processes

“…( 2020 ) investigated multiple cohorts in two different countries. Recently, Jevtić and Regis ( 2019 , 2021 ) developed a general multi-population model in a continuous-time setting using affine processes. In this work, we further contribute to the stream of literature concerning multi-population modeling by proposing a multi-population model with a deterministic component of a Poisson generalized linear model (see Renshaw et al.…”

Modelling USA Age-Cohort Mortality: A Comparison of Multi-Factor Affine Mortality Models

“…Alai et al (2019) show that the Gamma distribution fits mortality intensities well, which is consistent with mortality heterogeneity, suggesting non-Gaussian models may improve model fit at older ages. Jevtić and Regis (2021) develop square-root latent factor affine mortality models and show how these models provide a good fit to UK mortality data. Cohort effects have been observed in age-period data for many countries, as discussed, for example, in Willets (2004), Cairns et al (2009) and Gallop (2008).…”

“…We focus on a single-cohort mortality curve. Extensions to multiple-cohort affine age-cohort mortality models are found in Jevtic et al (2013), Chang and Sherris (2018), Jevtić and Regis (2019), Xu et al (2020a), andRegis (2021). We model the older ages of a single cohort using age-cohort mortality data.…”

“…The five models we consider and compare include a canonical affine mortality model; an Arbitrage-Free Nelson-Siegel (AFNS) mortality model (Christensen et al 2011) with identifiable factors of level, slope, and curvature of the mortality curve; and a mortality model based on the Cox-Ingersoll-Ross (CIR) model (Cox et al 1985;Jevtić and Regis 2021), allowing for a gamma distribution for mortality rates. We also investigate the impact of incorporating factor dependence to capture correlations for the Gaussian mortality models, giving another two models.…”