Quantifying longevity risk in annuities by means of the generalized age-period-cohort model

Quantifying longevity risk in annuities by means of the generalized age-period-cohort model

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Speaker: Peter Vekas

Hunt and Blake (2015) and Villegas et al. (2016) have recently created an attractive unifying framework of several popular mortality forecasting techniques (including the Poisson variant of the famous Lee - Carter model as well as the Cairns - Blake - Dowd, Age - Period - Cohort, Plat and Renshaw - Haberman models), which has been dubbed the Generalized Age - Period - Cohort (GAPC) family of models. We have applied the GAPC framework on a long time series of 50 years of official Hungarian age-specific mortality rates of people aged at least 65 years, performed model selection based on several popular criteria from the literature, and estimated the life expectancy at the retirement age of 65 years and the net single premium of an annuity starting at retirement. We compare our results to the values obtained by the assumption of static mortality rates as well as to earlier results from the literature. Weselect the best model based on the out-of-sample forecasting accuracy of five popular mortality forecasting techniques, and conclude that the Cairns - Blake - Dowd (2006) model provides the best predictive performance based on several widespread statistical criteria. For the sake of methodological correctness, we model parameter uncertainty using semi-parametric bootstrapping. Finally, we quantify the financial impact of ignoring longevity risk in life annuities, and based on a survey of earlier results, we argue that the role of longevity risk in Hungary has increased significantly in the past eight years. Beyond its global significance, we argue that this question is highly relevant in Europe due to the recent introduction and practical implementation of the Solvency II framework, which sets statutory solvency capital requirements for longevity risk, as well as in Hungary due to a new local law enabling voluntary pension fund members (about 1.5 million individuals) to convert their third-pillar retirement savings into annuities.

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