Bridging the Li-Carter's gap: a locally coherent mortality forecast approach.

Summary Countries with common features in terms of social, economic and health systems generally have mortality trends which evolve in a similar manner. Drawing on this, many multi-population models are built on a coherence assumption which inhibits the divergence of mortality rates between two populations, or more, on the long run. However, this assumption may prove to be too strong in a general context, especially when it is imposed to a large collection of countries. We also note that the coherence hypothesis significantly reduces the spectrum of achievable mortality dispersion forecasts for a collection of populations when comparing to the historical observations. This may distort the longevity risk assessment of an insurer. In this paper, we propose a new model to forecast multiple populations assuming that the long-run coherent principle is verified by subgroups of countries that we call the "locally coherence" property. Thus, our specification is built on a trade-off between the Lee-Carter's diversification and Li-Lee's concentration features and allows to fit the model to a large number of populations simultaneously. A penalized vector autoregressive (VAR) model, based on the elastic-net regularization, is considered for modeling the dynamics of common trends between subgroups. Furthermore, we apply our methodology on 32 European populations mortality data and discuss the behavior of our model in terms of simulated mortality dispersion. Within the Solvency II directive, we quantify the impact on the longevity risk solvency capital requirement of an insurer for a simplified pension product. Finally, we extend our model by allowing populations to switch from one coherence group to another. We then analyze its incidence on longevity hedges basis risk assessment. JEL Classification: C18, C32, C53, J11.