Consistent Dynamic Affine Mortality Models for Longevity Risk Applications

Abstract

This paper proposes and calibrates a consistent multi-factor affine term structure mortality model for longevity risk applications. We show that this model is appropriate for fitting historical mortality rates. Without traded mortality instruments the choice of risk-neutral measure is not unique and we fit it to observed historical mortality rates in our framework. We show the risk-neutral parameters can be calibrated and are relatively insensitive of the historical period chosen. Importantly, the framework provides consistent future survival curves with the same parametric form as the initial curve in the risk-neutral measure. The multiple risk factors allow for applications in pricing and more general risk management problems. A state-space representation is used to estimate parameters for the model with the Kalman filter. A measurement error variance is included for each age to capture the effect of sample population size. Swedish mortality data is used to assess 2- and 3-factor implementations of the model. A 3-factor model specification is shown to provide a good fit to the observed survival curves, especially for older ages. Bootstrapping is used to derive parameter estimate distributions and residual analysis is used to confirm model fit. We use the Heath-Jarrow-Morton forward rate framework to verify consistency and to simulate cohort survivor curves under the risk-neutral measure.

Keywords: mortality model, longevity risk, multi-factor, affine, arbitrage-free, consistent, Kalman Filter, Swedish Mortality

JEL Classification: G12, G22, G23, C13, C51, C52, J11