Lee-Carter error matrix simulation: heteroschedasticity impact on actuarial valuations

Abstract

Recently a number of approaches have been developed for forecasting mortality. In this paper, we consider the Lee-Carter model and we investigate in particular the hypothesis about the error structure implicitly assumed in the model specification, i.e., the errors are homoschedastic. The homoschedasticity assumption is quite unrealistic, because of the observed pattern of the mortality rates showing a different variability at old ages than younger ages. Therefore, the opportunity to analyse the robustness of estimated parameter is emerging. To this aim, we propose an experimental strategy in order to assess the robustness of the Lee-Carter model by inducing the errors to satisfy the homoschedasticity hypothesis. Moreover, we apply it to a matrix of Italian mortality rates. Finally, we highlight the results through an application to a pension annuity portfolio.