Nonparametric Estimation Of Quantile Regression And The Application Of Value At Risk In Foreign Exchange Field

Value at Risk(VaR)is currently the main tool used to measure market risk in VaRious risk management systems in the financial market.From the perspective of econometrics,VaR is the quantile of the distribution of return loss over a given level of confidence and holding period in financial risk management.In the method of estimating VaR,parameter estimation methods based on assumption that the yield rate is subject to a certain distribution are the most common.Therefore,in the common method of calculating VaR,it is very important to make correct assumptions about the statistical distribution of the return rate of financial assets.In conjunction with financial time series data,in this paper we use quantile regression,a method that does not require assumptions about data distribution in advance to study VaR.This paper attempts to propose a new method for calculating VaR based on the conditional autoregressive risk value(CAViaR)model.CAViaR is a method for calculating quantiles similar to the generalized autoregressive conditional heteroscedasticity(GARCH)form proposed by Engle and Manganelli in 2004.Based on the CAViaR model,this paper regards the link function that reveals the different evolutionary relationship between the quantile and the historical information as a dynamic function,and tries to use a nonparametric estimation method to approximate the link function.This paper proposes the use of non-parametric regression spline and smooth spline method to estimate the link function.In the selection of the smoothing parameters,we use the Schwarz Information Criterion(SIC)to select the location and number of the knots of the regression spline and the adjustment coefficient of the smoothing spline.Finally,using the model proposed in this paper,we conduct an empirical study on the value of China's foreign exchange market,and compare this method with other common methods for calculating VaR.