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 K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Weining Wang

Humboldt University of Berlin

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 K. 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 K. Härdle (Contact Author)

Humboldt University of Berlin - Institute for Statistics and Econometrics ( 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

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

Unter den Linden 6
Berlin, D-10099
Germany

Weining Wang

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

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