Stochastic modeling of assets and liabilities with mortality risk

Abstract

This paper describes a general approach for the stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income instruments including short- and long-maturity fixed-rate bonds as well as index-linked and corporate bonds. On the liability side, the risks are driven by future mortality developments as well as price and wage inflation. All the risk factors are modeled as a multivariate stochastic process that captures the dynamics and the dependencies across different risk factors. The model is easy to interpret and to calibrate to both historical data and to forecasts or expert views concerning the future. This feature is particularly useful in unprecedented circumstances like pandemics when historical data alone does not give a reasonable description of the future. The simple structure of the model allows for efficient computations. The construction of a million scenarios takes only a few minutes on a personal computer. The approach is illustrated with an asset-liability analysis of a defined benefit pension fund, pre- and post-COVID-19.