Copula Quantile Regression and Measurement of Risk in Finance

Abstract

Quantile regression is a basic tool for estimating conditional quantiles of a response variable Y given a vector of regressors X. It can be used to measure the effect of regressors not only in the center of a distribution, but also in the upper and lower tails. In this paper we use the Archimedean Copula nonlinear conditional quantile regression model to measure the tail area risk dependence in Shanghai and Shenzhen stock markets with 600 groups of data of daily closing prices from January 4, 2005 to August 21, 2007. And then the result of this method is compared with the tail dependence measure by extreme value method. The results derived from quantile regression method show that Shanghai and Shenzhen stock markets have different risk dependence under different quantiles. While extreme value theory method only focuses on the estimation of tail dependence and it also shows that Shanghai and Shenzhen stock markets have strong dependence in the lower tail.