Stochastic mortality models are important for a variety of actuarial tasks, from best-estimate forecasting to assessment of risk capital requirements. However, the mortality shock associated with the Covid-19 pandemic of 2020 distorts forecasts by (i) biasing parameter estimates, (ii) biasing starting points, and (iii) inflating variance. Stochastic mortality models therefore require outlier-robust methods for forecasting. Objective methods are required, as outliers are not always obvious on visual inspection. In this paper we look at the robustification of three broad classes of forecast: univariate time indices (such as in the Lee-Carter and APC models); multivariate time indices (such as in the Cairns-Blake-Dowd and newer Tang-Li-Tickle model families); and penalty projections (such as with the 2D P-spline model). In each case we identify outliers using quantitative methods, then co-estimate outlier effects along with other parameters. Doing so removes the bias and distortion to the forecast caused by a mortality shock, while providing a robust starting point for projections. Illustrations are given for various models in common use.

Mortality shocks such as the one induced by the COVID-19 pandemic have substantial impact on mortality models. We describe how to deal with them in the period effect of the Lee–Carter model. The main idea is to not rely on the usual normal distribution assumption as it is not always justified. We consider a mixture distribution model based on the peaks-over-threshold method, a jump model, and a regime switching model and introduce a modified calibration procedure to account for the fact that varying amounts of data are necessary for calibrating different parts of these models. We perform an extensive empirical study for nine European countries, comparing the models with respect to their parameters, quality of fit, and forecasting performance. Moreover, we define five exemplary scenarios regarding the future development of pandemic-related mortality. As a result of our evaluations, we recommend the peaks-over-threshold approach for applications with a possibility of extreme mortality events.

The COVID-19 pandemic interrupts the relatively steady trend of improving longevity observed in many countries over the last decades. We claim that this needs to be addressed explicitly in many mortality modelling applications, for example, in the life insurance industry. To support this position, we provide a descriptive analysis of the mortality development of several countries up to and including the year 2020. Furthermore, we perform an empirical and theoretical investigation of the impact a mortality jump has on the parameters, forecasts and implied present values of the popular Lee–Carter mortality model. We find that COVID-19 has resulted in substantial mortality shocks in many countries. We show that such shocks have a large impact on point and interval forecasts of death rates and, consequently, on the valuation of mortality-related insurance products. We obtain similar findings under the Cairns–Blake–Dowd mortality model, which demonstrates that the effects caused by COVID-19 show up in a variety of models. Finally, we provide an overview of approaches to handle extreme mortality events such as the COVID-19 pandemic in mortality modelling.