Impact of longevity risk with best fit mortality forecasting model

Abstract

The data used in this research is from the Human Mortality database for the United States for the period 2000 - 2009. We first begin by fitting linear, Makeham, cubic smoothing spline and Lee Cater models to the data to establish which model best fits the data. Parameters are estimated using linear regression, graphical method and Singular Value Decomposition methods for the linear, Makeham and Lee Carter models respectively. By use of goodness of fit tests conducted using chi square, Cramer Von Mises criterion, Kolmogorov Smirnov and Anderson Darling tests, a best fit model to the data is established. Using standard error measures, best forecast model for the data is identified among the forecast methods, Cubic smoothing spline, ARIMA (Auto Regressive Integrated Moving Average) models with and without drift. Mortality rates based on the best fit model are forecasted to five year horizon using best forecasting method to the data. These rates are used to check if there has been a decline in mortality rates over the years. Impact of mortality decline (longevity risk) is then illustrated by calculation of Actuarial Present Values (APVs) of whole life annuity of a 60 year old male over the years.