Affine Mortality Models with Jumps: Parameter Estimation and Forecasting

Abstract: In this paper, we investigate the dynamics of age-cohort survival curves under the assumption that the instantaneous mortality intensity is driven by an affine jump-diffusion (AJD) process. Advantages of an AJD specification of mortality dynamics include the avail- ability of closed-form expressions for survival probabilities afforded by an affine mortality specification and the ease with which we can incorporate sudden positive and negative shocks in mortality dynamics, reflecting events such as wars, pandemics, and medical advancements. As we are interested in modelling the evolution of mortality rates, we propose a state-space approach to calibrate the parameters of the affine mortality process. This ensures consistent survival curves in the sense that forecasts of survival probabilities have the same parametric form as the fitted survival curves. As the resulting state-space model is non-Gaussian due to the presence of jumps, we apply and assess a particle filter-based Markov chain Monte Carlo approach to estimate the model parameters. We illustrate our methodology by fitting one- factor Cox-Ingersoll-Ross and Blackburn-Sherris mortality models with asymmetric double exponential jumps to historical age-cohort mortality data from USA. We find that these one-factor models with jumps have good in-sample fit, but their forecasting performance suggests the need for additional latent factors to improve the accuracy of forecasts.

Key words: Affine mortality models, affine jump-diffusion, age-cohort mortality rates, particle filter, particle Markov chain Monte Carlo