The Application of Affine Processes in Multi-Cohort Mortality Model

Cohort effects have been identified in many countries. However, some mortality models only consider the modelling and projection of age-period effects. Others, that incorporate cohort effects, do not consider cohort specific survival curves that are important for pricing and hedging purposes. In this paper, we consider modelling mortality development on a cohort basis, propose and assess a multi-cohort mortality model in an affine framework. We model the mortality intensity with common factors that affect all the cohorts as well as cohort specific factors that only affect specific cohorts, so that the correlations among cohorts are not perfect.In particular, we consider a three-factor case. The three-factor multi-cohort model is established using Danish male mortality data. The two common factors are extracted using a Kalman Filter algorithm and cohort specific factors are estimated by minimizing the residual calibration error. The calibration results demonstrate the need for cohort effects. The out-of-sample forecast performance of the proposed model, the RH model (age-period-cohort model developed of Renshaw and Haberman (2006)) and the CBD model (age-period model developed of Cairns et al. (2006)) are compared to actual mortality data. The results show that the proposed model produces more consistent estimates of cohort survival curves