Reference Work Entry

Handbook of Financial Econometrics and Statistics

pp 1467-1489

Date:

Quantile Regression in Risk Calibration

  • Shih-Kang ChaoAffiliated withLadislaus von Bortkiewicz Chair of Statistics, C.A.S.E. – Center for Applied Statistics and Economics, Humboldt–Universität zu Berlin Email author 
  • , Wolfgang Karl HärdleAffiliated withLadislaus von Bortkiewicz Chair of Statistics, C.A.S.E. – Center for Applied Statistics and Economics, Humboldt–Universität zu BerlinLee Kong Chian School of Business, Singapore Management University
  • , Weining WangAffiliated withLadislaus von Bortkiewicz Chair of Statistics, C.A.S.E. – Center for Applied Statistics and Economics, Humboldt–Universität zu Berlin

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