Semi-parametric extensions of the Cairns–Blake–Dowd model: a one-dimensional kernel smoothing approach

Over the last few decades, there has been an enormous growth in mortality modeling as the field of mortality risk and longevity risk has attracted great attention from academic, government and private sectors. In this paper, we propose a time-varying coefficient (TVC) mortality model aiming to combine the good characteristics of existing models with efficient model calibration methods. Nonparametric kernel smoothing techniques have been applied in the literature of mortality modeling and based on the findings from Li et al.’s (2015) study, such techniques can significantly improve the forecasting performance of mortality models. In this study we take the same path and adopt a kernel smoothing approach along the time dimension. Since we follow the model structure of the Cairns–Blake–Dowd (CBD) model, the TVC model we propose can be seen as a semi-parametric extension of the CBD model and it gives specific model design according to different countries’ mortality experience. Our empirical study presented here includes Great Britain, the United States, and Australia amongst other developed countries. Fitting and forecasting results from the empirical study have shown superior performances of the model over a selection of well-known mortality models in the current literature.