Revisiting key mortality rate models: novel findings and application of CIR processes to describe mortality trends

Several recent research papers have suggested using improvement mortality rates models instead of directly examining mortality rates to fit and forecast mortality. Modelling improvement mortality rates has been a common practice in actuarial companies, often used to construct new life tables or to assess longevity risk for insurers and pension schemes. Therefore, in this study, we align with this branch of literature by adapting the improvement mortality model proposed by Atance and Navarro (Financ Innov 10:61, 2024), where improvements in mortality rates are assumed to linearly depend on a small number of key age mortality rates. Specifically, we consider two alternative hypotheses for the number of deaths (Binomial and Poisson) to model mortality improvement rates. We employed the maximum likelihood criterion to estimate model parameters and identify the key mortality rate. Additionally, we propose using a Cox-Ingersoll-Ross (CIR) process to project the expected values of mortality rates. We present both in-sample and out-of-sample measures of fitting accuracy and forecasting ability for this model. We compare it with several alternative mortality models, using data from Spain and Italy for the age range 50–99 during the period 1975 to 2019.