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

Abstract:
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.

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

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