A Generalised GARCH-based Model for Stochastic Mortality

In this paper, we develop a generalised GARCH-based stochastic mortality model with a view to incorporate conditional heteroskedasticity and conditional non-normality in stochastic mortality modelling. We provide an empirical analysis of the UK mortality rates from 1922 to 2009 and find that both features are long-term behaviour of mortality structures. These structures impact the valuation and hedging of longevity-related insurance products and have been largely overlooked in many existing literature except for a very recent work by Giacometti et. al (2012), where only conditional heteroskedasticity is considered. To describe conditional non-normality, we adopt a Double Exponential distribution, also capable of incorporating the conditional skewness and leptokurtosis in our dataset. For the practical implementation, as in Siu, Tong and Yang (2004), we propose a user-friendly two-stage estimation scheme. At the first stage, we employ the Quasi-Maximum Likelihood Estimation (QMLE) to estimate the GARCH structure whilst at the second stage we adopt the MLE to estimate the Double Exponential parameters using residuals as inputs. We also examine the forecasting performance of the proposed model and find that the Double Exponential GARCH model provides reasonably good forecasts for future mortality developments.