This special issue of the Journal of Demographic Economics contains 10 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity 16: The Sixteenth International Longevity Risk and Capital Markets Solutions Conference that was held in Helsingør near Copenhagen on 13–14 August 2021. It was hosted by PerCent at Copenhagen Business School and the Pensions Institute at City, University of London.

Pension risk transfer and longevity risk transfer are now growing secular trends. From North America to Europe, companies are de-risking pension plans in near-record volumes and have continued to boldly do so throughout the pandemic—at or near the most favorable pricing experienced in years. The arrival of funded reinsurance on both sides of the Atlantic is bringing reinsurer capital and private assets to support the steady growth in the pension risk transfer market. Additionally, we have observed that the enduring low-rate environment and quest for uncorrelated risk has the world's largest investors directing billions into life reinsurance sidecars. How have these markets thrived during the worst global outbreak in a century? Key research on the pandemic's impact on pensioner life expectancy allowed prices to be set and transactions to proceed through a time of significant uncertainty.

Longevity risk is the risk that people on average will live longer than expected. That potential increase in life expectancy exposes corporations and pension funds to the risk of having insufficient funds to pay a more extended stream of annuity benefits. Buy-ins, buy-outs, and longevity bonds provide pension funds with insurance and financial market instruments to hedge their longevity risk. The most straightforward instruments and the most robust markets are currently for buy-ins and buy-outs. The model developed here shows that these instruments transfer value to pension holders and, other things being equal, would not be used by firms since shareholder value is reduced. The analysis, however, also shows that these instruments can be used to solve the under-investment problem created by underfunded pension plans and so increase not only the pension fund value but also the corporate stock value.

This paper provides a new market consistent approach to the valuation of no negative equity guarantees and equity release mortgages. The paper provides a new approach to the estimation of volatility inputs. The proposed approach to volatility produces a volatility term structure that is dependent on the age and gender of the borrower. Illustrative valuations are provided based on the Black ’76 put pricing formula and mortality projections based on the M5 Cairns–Blake–Dowd mortality model. Results show interesting ramifications for industry practice and prudential regulation.

It is well-known that marital status is an important predictor for life expectancy. However, non-married individuals are often misclassified as singles which ignores the heterogeneity within the group. This paper shows the importance of distinguishing between types of singles, and in particular whether they are cohabiting, when predicting life expectancies. We use unique and detailed longitudinal register data to track marital status throughout the individual's lifetime. We find that all types of singles consistently benefit from living with a spouse, i.e., after divorce, becoming widower or being never married. This result holds for both men and women. For certain types of cohabiting singles we reject significant differences in life expectancy compared to married individuals. Finally, we use a case study to show that, like married individuals, all types of singles that cohabit also serve as informal caregivers and have the potential to limit the end-of-life long-term care expenditure levels.

An ageing population increases pressure on health and social care, welfare payments and pensions in public funded systems. There is no simple measure linking population health to economic disadvantage or the resulting tax burden. We imagine a situation in which local areas are responsible for financing their own public services. We hypothesize a local tax is levied to cover healthcare costs, welfare benefits for those who are sick, and pensions. We partition the costs based on years spent in ill health, disability and pensionable years over the life course using the average costs per person per year for each. We argue that area differences in tax rates provide a summary measure of inequality since a higher tax burden would fall on areas least able to afford it. We show that a one year improvement in healthy life expectancy would add 4.5 months to life expectancy (LE) and 3.4 months to working lives whilst reducing taxes by around 0.5%. We cast doubt on the target to increase health expectancy by five years by 2035; however, were it to be achieved it would add 23 months to LE, 17 months to work expectancy and reduce taxes by 2.4%.

This study considers data from 5 waves of the English Longitudinal Study of Ageing (ELSA). We aim to study the impact of demographic and self-rated health variables including disability and diseases on the survival of the population aged 50+. The disability variables that we consider are mobility impairment, difficulties in performing Activities of Daily Living (ADL) and Instrumental Activities of Daily Living (IADL). One of the problems with the survey study is missing observations. This may happen due to different reasons, such as errors, nonresponse and temporary withdrawals. We address this problem by applying single and multiple imputation methods. We then fit a Generalized Linear model (GLM) and Generalized Linear Mixed model (GLMM) to our data and show that a GLMM performs better than a GLM in terms of information criteria. We also look at the predictability of our models in terms of the time-dependent receiver operating characteristic (ROC) and the area of ROC, i.e. AUC. We conclude that among the disability factors, IADL and among the diseases, cancer significantly affect the survival of the English population aged 50 and older.

Cancer is among the leading causes of death in the world, with about 10 million deaths, one in every six deaths, related to cancer in 2020. In Taiwan, cancer insurance is the most popular commercial health product. However, the loss ratio of cancer products increases with policy year and exceeds 100% in many insurance companies. In addition, almost all cancer benefits are significantly limited in order to avoid financial insolvency. In this study, we evaluate the risk of cancer insurance from the perspective of morbidity compression. We use the data from Taiwan's National Health Insurance Research Database. Also, we apply the standardized mortality ratio and the Lee-Carter model to estimate the trend of cancer-related values. We find that cancer incidence rates gradually increase with time, which indicates that the assumption of morbidity compression is violated. On the other hand, the mortality rates of cancer patients decrease significantly annually. Thus, length of life with cancer increases, and so does the cancer insurance premium. We suggest that cancer insurance covers only the first five years of medical expenditure after the insured is diagnosed with cancer.

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 starting point of our research is the inadequacy of assuming, in the construction of a model of mortality, that frailty is constant for the individuals comprising a demographic population. This assumption is implicitly made by standard life table techniques. The substantial differences in the individual susceptibility to specific causes of death lead to heterogeneity in frailty, and this can have a material effect on mortality models and projections—specifically a bias due to the underestimation of longevity improvements. Given these considerations, in order to overcome the misrepresentation of the future mortality evolution, we develop a stochastic model based on a stratification weighting mechanism, which takes into account heterogeneity in frailty. Furthermore, the stratified stochastic model has been adapted also to capture COVID-19 frailty heterogeneity, that is a frailty worsening due to the COVID-19 virus. Based on different frailty levels characterizing a population, which affect mortality differentials, the analysis allows for forecasting the temporary excess of deaths by the stratification schemes in a stochastic environment.

In multi-population mortality modeling, autoregressive moving average (ARMA) processes are typically used to model the evolution of mortality differentials between different populations over time. While such processes capture only short-term serial dependence, it is found in our empirical work that mortality differentials often exhibit statistically significant long-term serial dependence, suggesting the necessity for using long memory processes instead. In this paper, we model mortality differentials between different populations with long memory processes, while preserving coherence in the resulting mortality forecasts. Our results indicate that if the dynamics of mortality differentials are modeled by long memory processes, mean reversion would be much slower, and forecast uncertainty over the long run would be higher. These results imply that the true level of population basis risk in index-based longevity hedges may be larger than what we would expect when ARMA processes are assumed. We also study how index-based longevity hedges should be calibrated if mortality differentials follow long memory processes. It is found that delta hedges are more robust than variance-minimizing hedges, in the sense that the former remains effective even if the true processes for mortality differentials are long memory ones.