For any fund manager, the ability to project expected returns into the futureis vital, but it poses a great deal of uncertainty. When the underlying risk istied to human longevity, the uncertainty is found in the stochastic nature of mortality.
This thesis presents two approaches to approximating a distribution of expected payoffs for a portfolio containing US life insurance policies. The first one utilizes the Monte Carlo method and approximates the payoff in binary and monetary values. The second approach uses the De Pril’s recursive algorithm to calculate the binary distribution. The different methods are evaluated on two key factors; accuracy and computational cost. In addition, different portfolio distributionsare evaluated in terms of their statistical characteristics and longevity exposure.
The results presented in this thesis indicate that the Monte Carlo method isthe more appropriate method for calculating payoff distributions of US life insurance portfolios. Although the De Pril’s method displays an accurate resultfor a single time period, the process of repeated convolution to evaluate longertime periods leads to an unsustainable increase in the error term. An analysis of statistical measurements indicates that life settlement portfolios have apeaky distribution with heavy tails and positive skewness. Furthermore, testsof longevity show that the portfolio distributions are sensitive to the accuracyof mortality assumptions.