基于非线性分位数回归模型的多期VaR风险测度

Evaluating Multiperiod VaR via Nonlinear Quantile Regression Model

多期VaR主要受到持有期及波动率两个变量的影响,并且其影响模式(线性或非线性)的确定对于准确地进行VaR风险测度至关重要。非线性分位数回归模型,能够克服线性分位数回归模型只能揭示多期VaR及其影响因素之间线性依赖关系的局限,从而提高多期VaR风险测度的准确性。结合波动模型与两个非线性分位数回归方法:QRNN和SVQR,给出了多期VaR风险测度的三类方案:波动模型法、QRNN+波动模型法、SVQR+波动模型法。选取3个股票价格指数作为研究对象,考虑了6种不同形式的波动模型,得到了18个多期VaR风险测度方法进行实证比较,结果表明:波动模型选择影响到多期VaR风险测度效果;SVQR+波动模型法略优于QRNN+波动模型法,并且两者显著优于波动模型法。

The stylized facts of financial markets,such as volatility clustering,fat tail and asymmetry,make the multiperiod VaR do not comply with simple ＂ rule of time root＂ in one period VaR measure.Therefore,a more reasonable method is need to seek to evaluate multiperiod VaR accurately.Multiperiod VaR is mainly influenced by two variables,i.e.holding period and volatility.To determine the impact model（linear or nonlinear）of the two variables is essential for evaluating VaR accurately.Nonlinear quantile regression model,overcoming the limitations of the linear quantile regression model in describing linear dependence between multiperiod VaR and its influencing factors,can be used to improve the accuracy of VaR.Three types of methods,volatility model,QRNN＋volatility model,and SVQR＋volatility model,for evaluating multiperiod VaR has been proposed in this paper based on volatility modeling and nonlinear quantile regression method.For empirical application,three stock price indices are selected：Shenzhen Composite Index,Hang Seng Index and SP 500 from 19Jan.2011 to 28Sep.2012.Six different volatility models are considered and two types of nonlinear quantile regression models are combined with them.As a result,the 18 kinds of methods in multiperiod VaR measure are compared together.The empirical results show that volatility model has an influence on the effect of multiperiod VaR measure.In terms of the accuracy of VaR measure,the SVQR＋volatility model is slightly better than QRNN＋volatility model,and both of them are superior to the volatility model.The good performance of the nonlinear quantile regression models in VaR evaluation comes from the fact that the QRNN and SVQR models belong to nonparametric methods.They have the ability to discover a complex nonlinear relationship among variables without specifying a explicit functional form.This property is very useful for exploring the unknown relation among financial variables.