Weekly, quarterly and yearly risk measures are crucial for risk reporting according to Basel III and Solvency II. For the respective data frequencies, the authors show in a simulation and backtest study that available data series are not sufficient in order to estimate Value at Risk and Expected Shortfall sufficiently, given confidence levels of 99.9% and 99.99%. Accordingly, this paper presents a semi-parametric estimation method, rescaling data from high- to low-frequency which allows to obtain significantly more data points for the estimation of the respective risk measures. The presented methodology in the α-stable framework, which is able to mimic multifractal behavior in asset returns, provides tail events which never occurred in the original low-frequency dataset.
high-frequency multifractal stable distribution rescaling risk management Value at Risk quantile distribution