Why the Deferred Annuity Makes Sense

The COVID-19 pandemic, along with other major pandemics such as HIV/AIDS and the 1918 influenza pandemic, has highlighted critical challenges and opportunities that continue to reshape global perspectives and responses. These events have also had notable implications for the actuarial profession, affecting all practice areas. Drawing from its work on pandemic-related issues, the International Actuarial Association (IAA) has identified several key themes that have emerged from examining the effects of pandemics on actuarial practice. To address these, the IAA’s Pandemic Task Force and the Mortality Virtual Forum have produced four key papers: - Lessons Learned from Pandemics - Implications of COVID-19 Protection Gaps - Implications of COVID-19 Data and Pandemic Modeling (to be released in Q1 2025) - Excess Deaths Analysis: A technical paper reviewing mortality data from 21 countries and exploring various methods for calculating excess deaths. This session aims to provide an overview of the IAA’s pandemic-related initiatives, foster understanding of the implications for the actuarial profession, and promote dialogue on the lessons learned from these global health crises and how the profession could prepare for the future.

Several stochastic mortality forecasting techniques, such as the Lee-Carter and Li-Lee models, extract a time-dependent mortality index from logarithmic mortality rates, while producing a residual noise term. These models typically forecast the index while discarding the noise. However, residuals may contain significant temporal, spatial, and spatio-temporal autocorrelation, offering valuable patterns that can be leveraged to improve forecasts. In this study, we propose a machine learning methodology to incorporate this autocorrelation into the mortality index and its forecasts. We introduce two hyperparameters: one regulates the strength of the enhancement, and the other specifies the adjustment method for the mortality index. The adjusted index can then be forecasted using traditional methods such as random walk, ARIMA, and vector autoregression, or more advanced techniques like spatial dynamic panel linear models, eigenvector spatio-temporal filters, and spatio-temporal ARIMA models. Special care is taken to ensure coherence in forecasts across multiple populations, particularly for the Li-Lee model. We apply the proposed methods to data from several countries, testing them on both the Lee-Carter and Li-Lee models. By optimizing the hyperparameters through a train-test-validation split, we compare forecasts with and without incorporating autocorrelational patterns. The results demonstrate that traditional models can be significantly improved by including this additional information. These refined forecasts offer substantial benefits for applications such as life insurance, annuities, pensions, and other areas dealing with longevity risk.