Empirical Scenario Forecasting for financial risk measurement in pension annuity systems

Within the life insurance framework, internal models have to be outlined both for Solvency Capital Requirement purposes and for portfolio performance management. The paper concerns in particular the pension annuity contracts, characterized by long durations and multiplicity of payments linked to the survival trend; in cases like these, description of the future financial and demographic scenario constitutes a great issue. Interest rates future evolution interacts with the uncertainty in future lifetimes due to the systematic effects of the longevity phenomenon. Regarding the demographic risk driver, in order to get more reliable and accurate mortality projections to the aim of the longevity improvement control, we use the semi parametric Stratified Sampling Bootstrap applied to the Lee Carter Poisson distribution. In the paper the question of the reduction of the variance estimator is fronted by means of Variance Reducing Techniques. We consider the financial status of a business line well described by the surplus indicator, given by the difference between the retrospective gains and the perspective loss and the study analyses the interplay between specific market consistent assumptions for interest rate structure and the dynamic demographic description deepening in particular its effects on the surplus. The model is implemented in the last section, in which the financial and demographic hypotheses are specified by simulation techniques to the aim of measuring the financial risk impacting on a pension annuity portfolio.