Quantile Estimation Of Extreme Conditions And Its Application In VaR Measurement

The risk value VaR is one of the most important methods in the financial world.Financial institutions regard VaR as an important index to predict and control risks.Quantile regression is widely used in VaR calculations,whereas traditional quantile regression is unstable at the tail,especially for heavy-tailed distribution caused by data sparsity.In order to solve the sparseness of financial data tails,this paper introduces an extreme conditional quantile estimation method based on extrapolation of intermediate order quantiles,and adds the Monte Carlo method to adjust the parameters.Numerical simulations show that the accuracy of the extreme value index and the extreme condition quantile is greatly improved compared with the previous process after adding the adjustment parameters.The empirical part takes the daily yield data of the America and Chinese stock markets as the research object,establishes an extreme conditional quantile estimation model,and estimates the extreme VaR of Bank of America stocks and the CSI 300 Index at very low quantile levels of 0.003 and 0.005.The results show that: first,the extreme conditional quantile of the daily yield of Bank of America stocks and the lag one day returns of Bank of America stocks,Dow Jones Industrial Average and Dow Jones US Financial Index all change in a positive direction,and the extreme conditions quantile of Bank of America stocks is most affected by its own lagging yield,which indicates that the past decline in Bank of America's stock price will drastically lower the extreme quantile of the current stock price;second,the CSI 300 Index and the previous day's yield of the Shanghai Composite Index have the same effect on the extreme conditional quantile of the daily yield of the CSI 300 Index.If the CSI 300 Index and the Shanghai Composite Index fell the previous day,then the CSI 300 Index will also have a downward trend on that day.Third,the extreme VaR of the Bank of America stock and the CSI 300 index at the 0.003 quantile level is measured and compared with the traditional quantile regression.The results show that the traditional quantile regression is more conservative and cannot measure extreme events well,and extrapolation based on extremum exponential estimation of extreme conditional quantiles can measure extreme VaR well.