Quantile Regression in Risk Calibration

SFB 649 Discussion Paper 2012-006

26 Pages Posted: 7 Jan 2017

See all articles by Shih-Kang Chao

Shih-Kang Chao

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

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin; Charles University; National Yang Ming Chiao Tung University; Asian Competitiveness Institute

Weining Wang

affiliation not provided to SSRN; University of York

Date Written: January 24, 2012

Abstract

Financial risk control has always been challenging and becomes now an even harder problem as joint extreme events occur more frequently. For decision makers and government regulators, it is therefore important to obtain accurate information on the interdependency of risk factors. Given a stressful situation for one market participant, one likes to measure how this stress affects other factors. The CoVaR (Conditional VaR) framework has been developed for this purpose. The basic technical elements of CoVaR estimation are two levels of quantile regression: one on market risk factors; another on individual risk factor. Tests on the functional form of the two-level quantile regression reject the linearity. A flexible semiparametric modeling framework for CoVaR is proposed. A partial linear model (PLM) is analyzed. In applying the technology to stock data covering the crisis period, the PLM outperforms in the crisis time, with the justification of the backtesting procedures. Moreover, using the data on global stock markets indices, the analysis on marginal contribution of risk (MCR) defined as the local first order derivative of the quantile curve sheds some light on the source of the global market risk.

Keywords: CoVaR, Value-at-Risk, quantile regression, locally linear quantile regression, partial linear model, semiparametric model

JEL Classification: C14, C21, C22, C53, G01, G10, G20, G32

Suggested Citation

Chao, Shih-Kang and Härdle, Wolfgang Karl and Wang, Weining and Wang, Weining, Quantile Regression in Risk Calibration (January 24, 2012). SFB 649 Discussion Paper 2012-006, Available at SSRN: https://ssrn.com/abstract=2894219 or http://dx.doi.org/10.2139/ssrn.2894219

Shih-Kang Chao

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

Spandauer Strasse 1
Berlin, D-10178
Germany

Wolfgang Karl Härdle (Contact Author)

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

Weining Wang

affiliation not provided to SSRN

University of York ( email )

Department of Economics and Related Studies Univer
York, YO10 5DD
United Kingdom

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