Backtesting the solvency capital requirement for longevity risk

Purpose - The determination of the capital requirements represents the first Pillar of Solvency II. The main purpose of the new solvency regulation is to obtain more realistic modelling and assessment of the different risks insurance companies are exposed to in a balance-sheet perspective. In this context, the Solvency Capital Requirement (SCR) standard calculation is based on a modular approach, where the overall risk is split into several modules and submodules. In Solvency II, standard formula longevity risk is explicitly considered. The purpose of this paper is to look at the backtesting approach for measuring the consistency of SCR calculations for life insurance policies. Design/methodology/approach - A multiperiod approach is suggested for correctly calculating the SCR in a risk management perspective, in the sense that the amount of capital necessary to meet company future obligations year by year until the contract will be in force has to be assessed. The backtesting approach for measuring the consistency of SCR calculations for life insurance policies represents the main contribution of the research. In fact this kind of model performance is generally specified in the VaR validation analysis. In this paper, this approach is considered for testing the ex post performance of SCR calculation methodology. Findings - The backtesting framework is able to measure, from time to time, if the insurer has allocated more or less capital to support his in-force business, with adverse effects on free reserves and profitability or solvency. Practical implications - The paper shows that the forecasting performance is an important aspect to assess the effectiveness of the model, a poor performance corresponding to a biased allocation of capital. Originality/value - The backtesting approach for measuring the consistency of SCR calculations for life insurance policies represents the main contribution of the research. In fact this kind of model performance is generally specified in the VaR validation analysis. Recently, Dowd et al. have proposed it for verifying the goodness of mortality models and now, in this paper, this approach is considered for testing the ex post performance of SCR calculation methodology.