Reducing Model Risk and Improving Mortality Forecasts for Life Insurance Product Pricing

Abstract

The pricing of life insurance products depends critically on the ability to model and forecast three core stochastic drivers. Firstly, the ability to accurately forecast expected mortality rates by age group for a given population in order to construct estimates of the life expectancy required for survival linked insurance products. Secondly, the ability to model interest rate dynamics accurately over multi-decade time horizons, and thirdly the ability to model the causal relationship between mortality events and interest rate fluctuations.

In this work we tackle all three aspects of these challenging problems faced by actuaries seeking to robustly price life products. We demonstrate with real data for three major populations, U.K., U.S.A. and Australia that we are able to reduce the model risk and associated forecast errors of classical Lee-Carter models in constructing forecasts for mortality and subsequent life expectancy by age and gender. This is achieved by developing new classes of multivariate long-memory models for mortality which we compare to extensions of classical Lee-Carter models. Secondly, we develop standard short rate one factor models for interest rates, in which we incorporate dependence links with our stochastic mortality models. We develop a Bayesian calibration and forecasting framework which is estimated with a Hamiltonian Markov Chain Monte Carlo sampling procedure.

We then utilise these frameworks to study the influence of model risk for life products including annuity portfolios and the valuation of a guaranteed annuity option (GAO). We demonstrate that classical Lee-Carter type models can produce less accurate model forecasts than our proposed multivariate long memory models and we quantify the mispricing cost of this model risk.

Keywords: Life Table, Gengenbauer Polynomial, Lee Carter Model, Long Memory, Bayesian Inference, Annuity Pricing, Guaranteed Annuity Option