Assessing Longevity Risk with Generalized Linear Array Models
Longevity risk is becoming more important in the current economic environment; if mortality improvements are larger than expected, profits erode in the annuity business and in defined benefit pension schemes. The Lee-Carter model, although a popular model for mortality rates by age and calendar year, has been critiqued for its inflexibility. A recently proposed alternative is to smooth the mortality surface with a generalized linear array model (GLAM), allowing for an additive surface of shocks. We compare the GLAM and Lee-Carter models by fitting them to Swedish mortality data. Lee-Carter mortality predictions are calculated, and a time series method for GLAM prediction is developed. The predicted mortality rates and associated uncertainties are then compared directly, but it is also useful to extend the comparison to annuities. Letting future mortality be stochastic, we can calculate the expectation and variance of the present value for various annuities.