Empirical Analysis On The Estimating Of Quantile Regression Model And The Tail Correlations Between Financial Risks

This discussion mainly discusses the application of Quantile Regression to the empirical estimating of conditional Value at Risk, Copula Quantile Regression model, and the applications of Copula functions to the empirical analysis of the tail correlations between financial risks.In this paper, the author apply Quantile Regression method to estimate conditional Value at Risk, i.e. VaR under some conditions, obtained directly with the value of the quantile under a certain confidence level of the distribution of the return rate. This estimating method obviously avoids the assumption that the return rate is normal distributed, and its calculation is relatively easy. Under a Quantile regression model including lag dummy variables, we empirically study the value at risk of Shanghai Composite Index and Shenzhen Composite Index on condition of daily volatility. By comparing with the corresponding results for models without conditions and linear Quantile Regression model, it shows that Quantile regression model with dummy variables is better to measure risk than those two classes of Quantile regression model.Additionally, the author also discuss Copula models and Copula Quantile regression in this paper. Several common Archimedean Copula Quantile curves are derived. Copula Quantile Regression combines Copula functions and the methods of quantile regression, which can better measure the relationship between variables, especially the tail correlation. Therefore, we apply Copula functions to the empirical analysis of the tail correlations between Hushen300and Shenzhen Composite Index. The up-tail correlation is quantified with an index, i.e., tail correlation coefficient. The empirical results show that there exists strong tail correlation between Hushen300index and Shenzhen composite index. Furthermore, the empirical study for GEM index and SSE SME Composite also discovers a strong tail correlation between these two indexes.