A Multivariate Forward-Rate Mortality Framework
24 Pages Posted: 18 Dec 2014 Last revised: 2 Jan 2015
Date Written: December 16, 2014
Stochastic mortality models have been developed for a range of applications from demographic projections to financial management. Financial risk based models build on methods used for interest rates and apply these to mortality rates. They have the advantage of being applied to financial pricing and the management of longevity risk. Olivier and Jeffery (2004) and Smith (2005) proposed a model based on a forward-rate mortality framework with stochastic factors driven by univariate gamma random variables irrespective of age or duration. We assess and further develop this model. We generalize random shocks from a univariate gamma to a univariate Tweedie distribution and allow for the distributions to vary by age. Furthermore, since dependence between ages is an observed characteristic of mortality rate improvements, we formulate a multivariate framework using copulas. We find that dependence increases with age and introduce a suitable covariance structure, one that is related to the notion of a minimum. The resulting model provides a more realistic basis for capturing the risk of mortality improvements and serves to enhance longevity risk management for pension and insurance funds.
Keywords: longevity risk, Olivier-Smith model, forward-rate mortality framework, minimum covariance pattern, copulas
JEL Classification: G23, G22, C58, C13
Suggested Citation: Suggested Citation