Data Driven Value-at-Risk Forecasting Using a SVR-GARCH-KDE Hybrid

IRTG 1792 Discussion Paper 2018-001

26 Pages Posted: 23 May 2018

See all articles by Marius Lux

Marius Lux

School of Business and Economics, Humboldt-University of Berlin

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin; Charles University; National Yang Ming Chiao Tung University; Asian Competitiveness Institute; Academy of Economic Studies, Bucharest

Stefan Lessmann

School of Business and Economics, Humboldt-University of Berlin

Date Written: December 13, 2017

Abstract

Appropriate risk management is crucial to ensure the competitiveness of financial institutions and the stability of the economy. One widely used financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear and parametric models can lead to biased results or even underestimation of risk due to time varying volatility, skewness and leptokurtosis of financial return series. The paper proposes a nonlinear and nonparametric framework to forecast VaR. Mean and volatility are modeled via support vector regression~(SVR) where the volatility model is motivated by the standard generalized autoregressive conditional heteroscedasticity (GARCH) formulation. Based on this, VaR is derived by applying kernel density estimation (KDE). This approach allows for flexible tail shapes of the profit and loss distribution and adapts for a wide class of tail events. The SVR-GARCH-KDE hybrid is compared to standard, exponential and threshold GARCH models coupled with different error distributions. To examine the performance in different markets, one-day-ahead forecasts are produced for different financial indices. Model evaluation using a likelihood ratio based test framework for interval forecasts indicates that the SVR-GARCH-KDE hybrid performs competitive to benchmark models. Especially models that are coupled with a normal distribution are systematically outperformed.

Keywords: Value-at-Risk, Support Vector Regression, Kernel Density Estimation, GARCH

Suggested Citation

Lux, Marius and Härdle, Wolfgang Karl and Lessmann, Stefan, Data Driven Value-at-Risk Forecasting Using a SVR-GARCH-KDE Hybrid (December 13, 2017). IRTG 1792 Discussion Paper 2018-001, Available at SSRN: https://ssrn.com/abstract=3176951 or http://dx.doi.org/10.2139/ssrn.3176951

Marius Lux

School of Business and Economics, Humboldt-University of Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin ( email )

Unter den Linden 6
Berlin, D-10099
Germany

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

Asian Competitiveness Institute ( email )

Singapore

Academy of Economic Studies, Bucharest ( email )

Bucharest
Romania

Stefan Lessmann (Contact Author)

School of Business and Economics, Humboldt-University of Berlin ( email )

Unter den Linden 6
Berlin, Berlin 10099
Germany

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