Actuarial Present Value and Variance for Changing Mortality and Stochastic Interest Rates

Abstract

Stochastic modeling of interest rates is expected to lead a better risk management in long-term investments due to the rapid changes and random fluctuations in the economies. Considering the fact that deterministic interest rate approach does not yield realistic future values, a country-specific stochastic model is aimed to fit the interest rates based on the United States Treasury Inflation Protected Securities (TIPS) at 10-year constant maturity by using time series techniques. Under the assumption that interest rate follows an ARMA(1, 1) model, the actuarial present value and its variance for a ten-year term life insurance policy are derived. Additionally, the stochastic mortality using Lee-Carter model for future mortality predictions is implemented to the U.S. Mortality tables over a period of 81 years. Based on these two stochastic patterns, the actuarial present value and the variance functions are calculated numerically for the years 2014 and forecasted for 2030. The accuracy of the proposed model is performed by assessing a comparative analysis with respect to a prespecified deterministic interest rate and mortality table.