Forecasting age- and sex-specific survival functions: application to annuity pricing

<p dir="ltr">This study introduces a functional principal component regression (FPCR) forecast- ing method to model and forecast age-specific survival functions observed over time. The age distribution of survival functions is an example of constrained data, the values of which lie within a unit interval, rather than a linear vector space. Such a constraint is usually dealt with through an invertible logit transformation that maps constrained onto unconstrained data in a linear space. Our novel approach applies a functional time series forecasting method to a time series of unconstrained data to produce point and interval forecasts. The forecasts are then converted back to the original scale via inverse logit transformation. Using data for age- and sex-specific survival functions for Australia, we investigate the point and interval forecast ac- curacies for various horizons. We conclude that the FPCR provides better forecast accuracy than the commonly used Lee–Carter (LC) method. Therefore, we apply FPCR to calculate annuity pricing and compare it with the market annuity price. We also extend the analysis to examine cumulative hazard functions in a similar manner.</p>