The Heteroscedasticity Impact on Actuarial Science: Lee Carter Error Simulation

Abstract

C19 Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. As regards the latter, recent work has focused on modelling the trend in mortality as a stochastic process. A popular method for modelling death rates is the Lee-Carter model. In this paper we gives an overview of the Lee Carter model and the feasibility of using it to construct mortality forecast for the population data. In particular, we focus on a sensitivity issue of this model and in order to deal with it, we illustrate the implementation of an experimental strategy to assess the robustness of the LC model. The next step, we experiment and apply it to a matrix of mortality rates. The results are applied to a pension annuity. There are investigating in particular the hypothesis about the error structure implicitly assumed in the model specification, after having assume that errors are homoscedastic. Analyzing the model it is estimated that the homoscedasticity assumption is quite unrealistic, because of the observed pattern of the mortality rates showing a different variability at different ages. Therefore, there is an emerging opportunity to analyze the strength of predictable parameter. The purpose of this study is a strategy in order to assess the strength of the Lee-Carter model inducing the errors to satisfy the homoscedasticity hypothesis. The impact of Lee Carter model on various financial calculations is the main focus of the paper. Furthermore, it is applied it to a matrix of mortality rates including a pension rate portfolio. The Albania model with the variables of death and birth is shown on this paper taken in consideration the Lee Carter Error.