Parameter Uncertainty In The Lee-Carter Model
This paper investigates the parameter uncertainty in the Lee-Carter model, which is a two-step procedure for estimating and forecasting mortality rates and hence life expectancies (Lee and Carter, 1992). Although the Lee-Carter model is frequently applied, actuaries often tend to ignore the uncertainty that arises when estimating the model parameters. More specifically, when executing the two-stage procedure of the Lee-Carter model for estimating and forecasting mortality, the estimated Kt index which represents the improvement in mortality over the years is often regarded as if it is a known quantity. Yet, this simplification does not represent the fact that the Kt values are prone to estimation uncertainty. Neglecting the parameter uncertainty may have consequences for risk management, especially under the Solvency II legislation. Therefore, this paper proposes a simulation study to investigate the true underlying parameter uncertainty in the Lee-Carter model, and focuses in particular on the identification of the Kt process. The simulation study enabled us to link the parameter uncertainty problem that arises when using the Lee-Carter model with the theory on errors-in-variables models, as these are the regression models that elucidate the measurement errors in the independent variables. The results in all simulation settings indicate that there is a noticeable estimation error. In two out of four simulation cases, the estimation error did influence the time series analysis procedure for identifying the right model specification of the Kt index.
This thesis is not available in full for reasons of confidentiality.