Hierarchical mortality forecasting with EVT tails: An application to solvency capital requirement

Abstract

In this paper, we propose a new framework to coherently produce probabilistic mortality forecasts by exploiting techniques in seasonal time-series models, extreme value theory (EVT), and hierarchical forecast reconciliation. In a hierarchical setting, coherent forecasts are those forecasts that add up in a manner consistent with the aggregation structure of the collection of time series. We are amongst the first to model and analyze U.S. monthly death data during the period from 1968–2019 to explore the seasonality and the age–gender dependence structure of mortality. Our results indicate that incorporating EVT and hierarchical forecast reconciliation greatly improves the overall forecast accuracy, which has important implications for life insurers in terms of rate making, reserve setting, and capital adequacy compliance. Using the solvency capital requirement (SCR) under Solvency II as an example, we show that the SCR calculated by our approach is considerably higher than those calculated by alternative models, suggesting that failing to account for extreme mortality risk and mortality dependence in the hierarchy can result in significantly underfunded problems for life insurers. We also find that our model can yield death forecasts that are largely consistent with actual observations in most of months in 2021 when death tolls surged due to COVID-19. This provides additional evidence of the effectiveness of our model for practical uses.