Longevity: A ‘Simple’ Stochastic Modelling of Mortality

All UK insurers exposed to longevity risk need to perform stress tests for their Individual Capital Assessment (ICA). Some have put in place deterministic models which are arguably too simple; others have developed stochastic models that can be demanding and complex. This paper presents a simple model to turn any deterministic mortality scenario into a stochastic model. We propose a simple model of stochastic variation that is easy to explain and to implement, which could be an alternative to and/or complete some of the well known models. The model can be applied to any best estimates of future mortality rates, as it aims to describe how longevity behaves around the projected expected values. The paper proposes a possible calibration on the England and Wales population mortality that produces a minimum indication of possible future variation and uses the results to validate the model's assumptions. Using sample portfolios and the stochastic model, we can simulate cash flows to determine the distribution of the net present values (NPV) of annuity outgo.