Evaluating Multiperiod VaR Of Securities Market Via Quantile Regression Model

The development of economic integration and financial globalization,makes the financial markets of various countries are closely linked.The opening of financial markets brings more choices and opportunities to investors and financial institutions,while it also makes financial institutions and investors face more risk.Therefore,in order to ensure the stable development of our economy,we must maintenance of financial security and control financial risks.With the diversified development of financial market,the accuracy of financial risk measurement is becoming more and more rigorous.How to measure the financial risk effectively becomes a key issue.As a mainstream method to measure risk,VaR model has been applied to manage risk by various financial institutions and regulators since it was proposed.In recent years,to find out effective methods scholars at home and abroad have begun to experiment different methods to evaluate VaR.According to the statistical theory,VaR is a quantile which corresponding to the tail distribution of the yield sequence,which can be measured by the quantile regression model.Quantile regression model don't need to make assumption for the distribution of yield in advance,for processing a sharp peaks and fat tail distributions of financial data has certain advantages,meanwhile it is a good way to deal with extreme events.To find out an accurate evaluation method of VaR,and considering the financial stylized facts,including harp peaks and fat tail,I give three methods to evaluate VaR,they are GARCH model,QR-GARCH model and QR-SV model.Those models based on different assumption about distribution.In order to compare the effectiveness of these three methods,the results of multiperiod VaR of the three methods are tested by mean square error and likelihood ratio test.The conclusion of this paper is:first,QR-GARCH model is better than GARCH model in evaluate multiperiod VaR.GARCH-T model is the worst performing model,however it do well when combined with quantile regression model.Second,for different sample and different confidence level,the appropriate model is different.When the confidence level is 95%,the QR-GARCH-GED model have a good performance for S&P500 and Hang Seng Index,and the QR-GARCH-T model ave a good performancefor for Shanghai Composite Index.When the confidence level is 99%,the QR-GARCH-N model ave a good performance for S&P500?Hang Seng Index and Shanghai Composite Index.Third,the quantile regression model,which no need to make assumptions about distribution characteristics in advance,can reduce the gap of VaR under diffirent distribution characteristics.Fourth,from the effectiveness perspective,the QR-GARCH model is better than QR-SV model.But from the stability of model selection,the QR-SV model is perform better.