Affine Mortality Models with Jumps: Parameter Estimation and Forecasting

Life insurance companies face a significant level of mortality risk, hence there is a pressing need to better understand the evolution of mortality and longevity in the population. In this work, we study 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 availability 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. Furthermore, we are interested in age-cohort mortality as age-cohort data is more well-suited to pricing longevity-linked financial and insurance products.

As we are interested in a term structure model of mortality rates, we propose a state-space approach to calibrate the parameters of the affine mortality process. The measurement equation is given by the affine representation of the age-cohort average force of mortality and the state-transition equation is given by a discretization of the continuous-time mortality intensity dynamics. Such approach results to consistent survival curves in the sense that forecasts of survival probabilities have the same parametric form as the fitted survival curves. This contrasts with earlier work on AJD mortality models where the model must be re-estimated for every cohort of interest. The presence of jumps in the mortality intensity process implies that the state-transition equation is non-Gaussian. To this end, we propose 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 the USA and examining their forecasting performance.

This work contributes to the methodological aspects of mortality modelling, with emphasis on a detailed implementation of the proposed parameter estimation and mortality forecasting methodology. This work also serves as a preliminary step towards designing and pricing longevity-linked products under stochastic mortality dynamics with jumps.

Find the Q&A here: Q&A on 'Mortality Models'