The Investigation of a Forward-Rate Mortality Framework

Abstract

Stochastic mortality models have been developed for a range of applications from demographic projections to financial management. Financial risk based models built on methods used for interest rates and apply these to mortality rates. They have the advantage of being applied to financial pricing and the management of longevity risk. Olivier and Jeffery (2004) and Smith (2005) proposed a model based on a forward-rate mortality framework with stochastic factors driven by univariate gamma random variables irrespective of age or duration. We assess and further develop this model. We generalize random shocks from a univariate gamma to a univariate Tweedie distribution and allow for the distributions to vary by age. Furthermore, since dependence between ages is an observed characteristic of mortality rate improvements, we formulate a multivariate framework using copulas. We find that dependence increases with age and introduce a suitable covariance structure, one that is related to the notion of ax minimum. The resulting model provides a more realistic basis for capturing the risk of mortality improvements and serves to enhance longevity risk management for pension and insurance funds.

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

“…Gaussian models do not capture mortality heterogeneity at older ages (Pitacco 2016). 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.…”