Estimating Low Sampling Frequency Risk Measure by High-Frequency Data

IRTG 1792 Discussion Paper 2019-003

27 Pages Posted: 31 Aug 2020

See all articles by Niels Wesselhöfft

Niels Wesselhöfft

Humboldt Universität zu Berlin | IRTG 1792

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Yang Ming Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Date Written: January 29, 2019

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 back-test 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, re-scaling 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 multi-fractal behavior in asset returns, provides tail events which never occurred in the original low-frequency data set.

Keywords: High-Frequency, Multi-Fractal, Stable Distribution, Re-Scaling, Risk Management, Value at Risk, Quantile Distribution

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

Suggested Citation

Wesselhöfft, Niels and Härdle, Wolfgang K., Estimating Low Sampling Frequency Risk Measure by High-Frequency Data (January 29, 2019). IRTG 1792 Discussion Paper 2019-003, Available at SSRN: https://ssrn.com/abstract=3658145

Niels Wesselhöfft (Contact Author)

Humboldt Universität zu Berlin | IRTG 1792 ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

Wolfgang K. Härdle

Blockchain Research Center ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

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