The Volatility of Mortality

Abstract

The use of forward models for the future development of mortality has been proposed by several authors. In this article, we specify adequate volatility structures for such models. We derive a Heath-Jarrow-Morton drift condition under different measures. Based on demographic and epidemiological insights, we then propose two different models with a Gaussian and a non-Gaussian volatility structure, respectively. We present a Maximum Likelihood approach for the calibration of the Gaussian model and develop a Monte Carlo Pseudo Maximum Likelihood approach that can be used in the non-Gaussian case. We calibrate our models to historic mortality data and analyze and value certain longevity-dependent payoffs within the models.