Matthias Börger, Jochen Russ, Johannes Schupp
Increasing life expectancy and thus decreasing mortality rates constitute a global trend that can be observed in almost all countries worldwide. Estimating the current rate at which mortality rates decrease and modeling the future rate of decrease is important for e.g. demographers and actuaries. This task is commonly referred to as mortality trend modeling.
In many applications however one needs to carefully distinguish between two different mortality trends: The actual (but unobservable) mortality trend (AMT) prevailing at a certain point in time and the estimated mortality trend (EMT) that an observer would estimate given the (observable) realized mortality up to that point in time. Since the AMT is not observable, an actuary or demographer might misestimate the AMT at any point in time. In particular, he would typically not be able to distinguish between a recent chance in the actual trend and a “normal” random fluctuation around the previous long term trend. Depending on the question at hand, the AMT or the EMT or both need to be considered and modeled in analyses.
The paper provides a clear definition of and distinction between the actual mortality trend and the estimated mortality trend, discusses their connection, and explains which of the two is relevant for which kind of question. Moreover, a numerically efficient combined model for both trends is specified and calibrated to mortality data. The model component for the actual mortality trend builds on recent findings that mortality appears to evolve log-linear over time with random changes in slope. The model component for the estimated mortality trend is specified such that, given the assumed dynamics for the actual mortality trend, the estimated mortality trend matches the actual trend as close as possible. This provides valuable information on how best estimate mortality assumptions should be derived from the available data in general.
Finally, we apply the combined model in practical examples and illustrate the importance of distinguishing between AMT and EMT. We show that, if the AMT is wrongfully assumed observable, the hedge effectiveness of a longevity hedge or the SCR for longevity risk are typically misestimated significantly.