Quantile Regression And Its Applications In Statistical Analysis Of The Log-return Series Of The Stock Prices And VaR Type Modelling

In this article, we apply the Quantile regression method to both the determining the empirical conditional distributions of log return series of some Chinese stock prices and the VaR type modelling in risk management.It has a long history to study the stylized features of the distribution of log return series in finance and numerous results about the unconditional distribution have been obtained, but very few results about the conditional distribution have been reported. The problem is not that the conditional distribution is not important but that traditional methods are not convenient to be applied to this issue. While the classic regression method can only provide us the first two moments of the conditional distribution, the quantileSregression can help us to fully determine the quantiles of the conditional distribution. This will deepen and enrich our knowledge about the log return distributions. As a demonstration, this article also carries out an extensive study of the conditional distribution of SA (600104, Shanghai Automotive Co.,Ltd) by quantile regression.The computation of VaR and ES is essentially the computation of quantile of return series. Therefore, having finished the quantile regression procedures, we can evaluate the VaR and ES almost with no effort. An example of calculating the VaR and ES is also given in this paper.