Backtesting the solvency capital requirement for longevity risk

The determination of capital requirements represents the first Pillar of Solvency II. In this framework the Solvency Capital Requirement (SCR) is defined as the amount of capital that an insurer needs in order to remain viable in the market and maintain its default probability below a certain level. The main purpose of the new solvency regulation is to obtain a more realistic modelling and assessment of the different risks insurance companies are exposed to. According to this regulation the SCR standard calculation in based on a modular approach where the overall risk is split into several modules and submodules for which SCRs are computed separately and then aggregated according to pre-specified correlation matrices. The European Commission for calibrating this standard model has recently published the Technical Specification of 5Th Quantitative Impact Study (QIS5) where the effects of the new capial requirements are analysed. Longevity risk is one of the major risks that an insurance company or a pension fund will have to deal with and it is expected that its importance will grow in the near future. In agreement with these considerations in Solvency II standard formula longevity risk is explicity considered representing a sub-module of the life underwriting risk module. In this paper we will refer exactly to the sub-module of longevity risk and we suggest a multiperiod forward approach for the correspondig SCR, that is, we estimate at issue time the solvency adequacy along the overall portfolio contract duration. Then we propose a backtesting framework for measuring the consistency of SCR calculations for life insurance policies. In particular to evaluate the performances of the SCR calculation methodologies we quantify the convergence of SCR forecasts through the time. Finally we provide graphical analysis and numerical evidences.