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Utilization of outlier-adjusted lee-carter model in mortality estimation on whole life annuities

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2019
Yavrum, Cem
Annuity and its pricing are very critical to the insurance companies for their financial liabilities. Companies aim to adjust the prices of annuity by choosing the forecasting model that fits best to their historical data. While doing it, there may be outliers in the historical data influencing the model. These outliers can be arisen from environmental conditions and extraordinary events such as weak health system, outbreak of war, occurrence of a contagious disease. These conditions and events impact mortality of populations and influence the life expectancy. So, using future mortality estimates that are not generated by the model that includes all of these factors, can influence on the financial strength of the life insurance industry. Therefore, these outliers should be taken into account as well while forecasting mortality rates and calculating annuity prices. Although there are many discrete and stochastic models that can be used to forecast mortality rates, the most widely known and used of these is Lee-Carter model [18]. Fundamentally, Lee-Carter model uses some time-varying parameters and age-specific components. The parameter, which is inspired and used by many other researchers, is the mortality index κt , that Lee and Carter take as the basis in their model. Once, mortality index is forecasted correctly, then death probabilities of individuals and the prices of annuity can be estimated. In case when there exist extremes in the mortality rates, outlier-adjusted model developed by Chan [7] can be used. This approach implements some iteration integrated in original LeeCarter model to find better model that fits to historical data. In this thesis, we aim to find out whether there is a difference between models that consider mortality jumps and models that do not take into account jumps effects in terms of annuity pricing. Finally, we test the annuity vii price fluctuations among different countries and come to conclusion on the effects of different models on country characteristics. For this comparison, Canada as a developed country with high longevity risk and Russia as an emerging country with jumps in its mortality history are considered. In addition to Canada and Russia, data of UK, Japan and Bulgaria are analyzed to provide ease of interpretation in terms of country characteristics. The results of this thesis support the usages of outlieradjusted models for specific countries in term of annuity pricing.