The impact of long memory in mortality differentials on index-based longevity hedges

In multi-population mortality modeling, autoregressive moving average (ARMA) processes are typically used to model the evolution of mortality differentials between different populations over time. While such processes capture only short-term serial dependence, it is found in our empirical work that mortality differentials often exhibit statistically significant long-term serial dependence, suggesting the necessity for using long memory processes instead. In this paper, we model mortality differentials between different populations with long memory processes, while preserving coherence in the resulting mortality forecasts. Our results indicate that if the dynamics of mortality differentials are modeled by long memory processes, mean reversion would be much slower, and forecast uncertainty over the long run would be higher. These results imply that the true level of population basis risk in index-based longevity hedges may be larger than what we would expect when ARMA processes are assumed. We also study how index-based longevity hedges should be calibrated if mortality differentials follow long memory processes. It is found that delta hedges are more robust than variance-minimizing hedges, in the sense that the former remains effective even if the true processes for mortality differentials are long memory ones.