Nonlinear Modeling of Mortality Data and Its Implications for Longevity Bond Pricing

Abstract

Human mortality has been improving faster than expected over the past few decades. This unprecedented improvement has caused significant financial stress to pension plan sponsors and annuity providers. The widely recognized Lee–Carter model often assumes linearity in its period effect as an integral part of the model. Nevertheless, deviation from linearity has been observed in historical mortality data. In this paper, we investigate the applicability of four nonlinear time-series models: threshold autoregressive model, Markov switching model, structural change model, and generalized autoregressive conditional heteroskedasticity model for mortality data. By analyzing the mortality data from England and Wales and Italy spanning the years 1900 to 2019, we compare the goodness of fit and forecasting performance of the four nonlinear models. We then demonstrate the implications of nonlinearity in mortality modeling on the pricing of longevity bonds as a practical illustration of our findings.