Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2019 003

Estimating low sampling frequency risk measure by high-frequency data

Niels Wesselhöfft
Wolfgang K. Härdle

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

high-frequency, multifractal, stable distribution, rescaling, risk management,
Value at Risk, quantile distribution

JEL Classification:
C14, C22, C46, C53, G32