Using Interest Rate Models to Improve Mortality Forecast

Abstract

Future evolution of mortality poses important challenges for life insurance, pension funds, public policy and fiscal planning. Indeed, when fair values, premium rates and risk reserves are computed, sound and accurate models to forecast stochastic longevity are needed. In this paper, we propose a methodological approach in order to improve the predictive accuracy of the existing survival models. The central idea is to model the ratio between the observed death rates and the corresponding fitted values obtained as outputs of a survival model we select, by means of the Cox-Ingersoll-Ross (CIR) model. For our numerical application, we choose to apply the CIR correction to the Cairns-Blake-Dowd (or M5) model. Using the Italian females mortality data and implementing the backtesting procedure, over both a static time horizon and fixed-length windows rolling one-year ahead through time, we empirically test the performance of the CBD model in forecasting death rates both for itself (CBD) and corrected by the CIR process (mCBD). On the basis of average measures of forecasting errors and information criteria we demonstrate that the mCBD model is a parsimonious model providing better results in terms of predictive accuracy than the CBD model.