Basis risk modelling: a co-integration based approach

Most mortality models are generally calibrated on national population. However, pensions funds and annuity providers are mainly interested in the mortality rates of their own portfolio. In this paper we put forward a multivariate approach for forecasting pairwise mortality rates of related population. The investigated approach links national population mortality to a subset population using an econometric model that captures a long-run relationship between both mortality dynamics. This model does not lay the emphasis on the correlation that the two given mortality dynamics would present but rather on the long-term behaviour, which suggests that the two time-series cannot wander off in opposite directions for very long without mean reverting force on grounds of biological reasonableness. The model additionally captures the short-run adjustment between the considered mortality dynamics. Our aim is to propose a consistent approach to forecast pairwise mortality and to some extent to better control and assess basis risk underlying index-based longevity securitization. An empirical comparison of the forecast of one-year death probabilities of portfolio-experienced mortality is performed using both a factor-based model and the proposed approach. The robustness of the model is tested on mortality rate data for England & Wales and Continuous Mortality Investigation assured lives representing a sub-population.