Scenario Generation with Stationary Block Bootstrap: An Application in the Solvency II Context

Abstract

We apply the technique of stationary block bootstrap (SBB) for scenario generation in the context of Solvency II. Insurance companies can develop a Solvency II internal model which often entails the generation of scenarios of shocks to risk factors and their dependence structure over a one-year horizon. Due to limited data, this is often performed using higher frequency data, e.g. monthly data. SBB is a form of historical simulation where blocks of historical data of random size between 1 to N (12 in case of monthly data) are randomly sampled and summed up until reaching N (12) blocks, thus generating scenarios of annual shocks. Temporal dependence such as autocorrelation and volatility clustering in historical data is captured in the block of data sampled. When applied to multiple risk factors simultaneously, SBB also captures the cross-sectional dependence in the data. As such, SBB can replicate the temporal dependence in and cross-sectional dependence across risk factors maximally with minimal modelling assumptions. We apply SBB to generate scenarios of market risk factors of equity and credit spread and show that the scenarios generated can replicate the shape in terms of skewness and kurtosis and the 1-in-200 event of the historical data to a good extent. We also apply SBB to the two risk factors simultaneously to generate copulas that capture the dependence structure of the two risk factors.