Colin O'Hare

Two-Dimensional Kernel Smoothing of Mortality Surface: An Evaluation of Cohort Strength

Accurate mortality forecasts are of primary interest to insurance companies, pension providers and government welfare systems due to the rapid increase in life expectancy during the past few decades. Existing mortality models in the literature tend to project future mortality rates by extracting the observed patterns in the mortality surface. Recently, patterns found in the cohort dimension have received a considerable amount of attention. However, to our best knowledge very few studies have considered an evaluation and comparison of cohort effect across different countries. Moreover, the answer to the question of how does the incorporation of cohort effect affect the forecasting performance of mortality models still remains unclear. In this paper we introduce a new way of incorporating cohort effect at the beginning of the estimation stage via the implementation of kernel smoothing techniques. Bivariate standard normal kernel density is used and we interpret cohort effect as the correlation in age and time dimensions. Based on the results from our empirical study, we compare and discuss the differences in cohort strength across a range of developed countries. Further, the fitting and forecasting results of the proposed model has been shown to outperform some well-known mortality models in the literature under a majority of circumstances.

Mortality Forecast: Local or Global?

Accurate future mortality forecasts are of fundamental importance as they ensure adequate pricing of mortality-linked insurance and financial products. Extrapolative methods are the most commonly adopted forecasting approach in the literature on projecting future mortality rates (see for example Clayton and Schifflers, 1987; Lee and Carter, 1992). There are generally two types of mortality models using the extrapolative approach. The first extracts patterns in age, time and cohort dimensions either in a deterministic fashion or a stochastic fashion (see for example Lee and Carter, 1992; Plat, 2009). The second uses non-parametric smoothing techniques to model mortality and thus has no explicit constraints placed on the model (see for example Currie, et al, 2004; Hyndman and Ullah, 2007). We argue that the main difference between the two types of models in terms of forecasting is the fact that, the former uses global information and the latter mainly uses local information. In this paper we conduct an investigation on the comparison of the forecasting performance of the two types of models using Great Britain male mortality data from 1950 to 2009. The paper assesses the accuracy of forecasts not only based on statistical measures but also take the randomness of residuals into account. A main conclusion from the study is that, local information seems to have greater predictive power over historical information so it should be given more weights in the forecasting process. We also conduct a robustness test to see how sensitive the forecasts are to the changes in the length of historical data used to calibrate the models.

Structural Breaks in Mortality Models: An International Comparison

In recent years the issue of life expectancy has become of upmost importance to pension providers, insurance companies and government bodies in the developed world. Significant and consistent improvements in mortality rates and hence life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data in order to anticipate future life expectancy and hence quantify the costs of providing for future ageing populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time and forecast these trends into the future using standard statistical methods. These approaches rely on the assumption that the direction of the linear trend will not change in the future, i.e. that structural breaks in the trend do not exist or do not have a significant impact on the mortality forecasts. Recent literature has started to question this assumption. In this paper we carry out a comprehensive investigation of the presence or otherwise of structural breaks in a selection of leading mortality models using data from 30 countries and for both males and females. We aim to identify how widespread the issue of structural breaks is in these types of models and hence comment on the validity of using such time series models in forecasting mortality rates. We find that structural breaks are present in a substantial (but not majority) of cases. Specifically, we find that structural breaks are more prevalent in male data than in female data and that the introduction of additional period factors in the model leads to a reduction in the presence of structural breaks in the main period effect. Where there is a structural break present allowing for it will produce significantly different forecasts and we conclude that the use of time series extrapolative models in forecasting mortality rates must be approached with caution.

The Impact of Parameter Uncertainty in Insurance Pricing and Reserve with the Temperature-Related Mortality Model

Changes in mortality rates have an impact on the life insurance industry, the financial sector (as a significant proportion of the financial markets is driven by pension funds), the governmental agencies, and the decision and policy makers. Thus, the pricing of financial, pension and insurance products that are contingent upon survival or death and which is related to the accuracy of central mortality rates is of key importance. Recently, a temperature-related mortality (TRM) model was proposed by Seklecka et al. (2017), and it has show evidence of outperformance compared with the Lee and Carter (1992) model and several other of its extensions, when mortality-experience data from the United Kingdom is used. There is a need for awareness, when fitting the TRM model, of model risk when assessing longevity-related liabilities, especially when pricing long term annuities and pensions. In this paper, the impact of uncertainty on the various parameters involved in the model is examined. We demonstrate a number of ways to quantify model risk in the estimation of the temperature-related parameters, the choice of the forecasting methodology, the structures of actuarial products chosen (e.g., annuity, endowment and life insurance), and the actuarial reserve. Finally, several tables and figures illustrate the main findings of this paper.

Structural Breaks in Mortality Models and their Consequences

In recent years the issue of life expectancy has become of upmost importance to pension providers, insurance companies and the government bodies in the developed world. Significant and consistent improvements in mortality rates and hence life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data in order to anticipate future life expectancy and hence quantify the costs of providing for future ageing populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age and cohort and forecast these trends into the future using standard statistical methods. The modeling approaches used fail to capture the effects of any structural change in the trend and thus potentially produce incorrect forecasts of future mortality rates. In this paper we look at a range of leading stochastic models of mortality and test for structural breaks in the trend time series.

Models of Mortality - Analysing the Residuals

The area of mortality modelling has received significant attention over the last 20 years owing to the need to quantify and forecast improving mortality rates. This need is driven primarily by the concern of governments, professionals, insurance and actuarial professionals and individuals to be able to fund their old age. In particular, to quantify the costs of increasing longevity we need suitable model of mortality rates that capture the dynamics of the data and forecast them with sufficient accuracy to make them useful. In this paper we test several of those models by considering the fitting quality and in particular, testing the residuals of those models for normality properties. In a wide ranging study considering 30 countries we find that almost exclusively the residuals do not demonstrate normality. Further, in hurst tests of the residuals we find evidence that structure remains that is not captured by the models.

Modelling Retirement Outcomes in Australia

Australias retirement income system obligates employers to pay a percentage of salary (currently 9.5%) on behalf of each employee directly into a superannuation fund which cannot be accessed (except in extraordinary circumstances) prior to the national minimum retirement age. The system has received strong praise for its high participation rates (driven by compulsion) and for ensuring retirees have resources from which they can support their own post-retirement lifestyle. However, recent discourse, particularly in the context of increasing life expectancy, has highlighted the potential inadequate level of savings provision under the superannuation systems current regulatory settings. In this paper we build a stochastic model of superannuation, the SUPA (Simulation of Uncertainty for Pension Analysis) model, and use this to simulate the evolution of superannuation fund balances across time. The lifetime of a superannuation account encompasses a growth phase followed by a withdrawal phase with the aspiration being that balances are positive throughout both phases. The model we develop consists of four elements: (i) a stochastic projection of investment returns; (ii) a stochastic projection of income levels (upon which contributions to the fund are based); (iii) a projection of levels of withdrawal in retirement; and (iv) a stochastic projection of increasing longevity. These four elements are described in detail within the paper. Combining these elements together the overall SUPA model, which extends previous models utilised in actuarial science, can inform the current superannuation debate. In particular, it can be used to forecast likely outcomes (i.e. whether individuals will have sufficient funds in retirement), under the current superannuation structures. It can also be used to statistically model the potential impacts of any changes to the superannuation system, i.e. changing retirement ages or contribution rates.