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

Abstract

Affine mortality models are well suited for theoretical and practical application in pricing and risk management of mortality risk. They produce consistent, closed-form stochastic survival curves allowing for the efficient valuation of mortality-linked claims. We model USA age-cohort mortality data using five multi-factor affine mortality models. We focus on three-factor models and compare four Gaussian models along with a model based on the Cox–Ingersoll–Ross (CIR) process, allowing for Gamma-distributed mortality rates. We compare and assess the Gaussian Arbitrage-Free Nelson–Siegel (AFNS) mortality model, which incorporates level, slope and curvature factors, and the canonical Gaussian factor model, both with and without correlations in the factor dynamics. We show that for USA mortality data, the probability of negative mortality rates in the Gaussian models is small. Models are estimated using discrete time versions of the models with age-cohort data capturing variability in cohort mortality curves. Poisson variation in mortality data is included in the model estimation using the Kalman filter through the measurement equation. We consider models incorporating factor dependence to capture the effects of age-dependence in the mortality curves. The analysis demonstrates that the Gaussian independent-factor AFNS model performs well compared to the other affine models in explaining and forecasting USA age-cohort mortality data.

Keywords

• mortality models
• continuous time
• cohort curve
• affine rates
• Kalman filter