Comparing and forecasting using stochastic mortality models: a Monte Carlo simulation

Abstract

Generalized Age-Period-Cohort Model (GAPC) has been widely accepted as a mean of modelling mortality improvement but the parameter risk associated with it raises problem on forecasting accuracy. Hence, this study aims to utilise the simulation strategy to account for variability and uncertainty in the point and interval mortality estimate by using mortality experience of Taiwan. This study also aim to identify the best mortality model for Taiwan data and further compute the ruin probability to assess the solvency risk. The results show that the error of point estimate could be minimized using simulation depending on the type of forecast statistics and models. The interval estimates on the other hand generally produce similar width in most cases as compared to those without using simulation, suggesting that simulation failed to increase forecast accuracy significantly in terms of interval estimate with exception on Haberman-Renshaw model with cohort effect in squared form (HRb) in high age female population projection. AgePeriod-Cohort (APC) model is found to be most suited to both gender population in Taiwan by focusing on its ability to generate biological plausible rate, goodness of fit and forecasting performance. The mortality forecast based on APC model is then used in virtual cash flow projection on an annuity portfolio. Result shows that Renshaw-Haberman (RH) model is more sensible in annuity pricing as its product produce least solvency risk besides showing that the risk is greatly contributed by women population of higher age in the case of Taiwan.