Stochastic modeling of mortality rates and Mortality-at-Risk forecast by taking conditional heteroscedasticity effect into account

Mortality and mortality rate have become the major issues in insurance industries, for instance, life insurance and pension fund. Such industries will, in particular, be concerned with the quantification of risk attached, say longevity risk, to insurance products that may receive severe impacts from the fall of mortality rate. In this paper, we model the mortality rate by using an Autoregressive (AR) model with a conditional heteroscedasticity effect. This effect is accommodated by a stochastic model of Autoregressive Conditional Heteroscedastic (ARCH) as well as a Stochastic Volatility Autoregressive (SVAR) model. Furthermore, we do forecasting of what so-called Mortality-at-Risk (MaR) by adopting the Value-at-Risk framework and its improvement. The calculation of the MaR forecast for those two models is conducted with significantly different approaches.