基于Levy-GARCH模型的股票市场尾部风险度量研究

Tail Risk Measurement in Stock Market Based on Levy-GARCH Model

防范化解金融风险是牢牢守住不发生系统性风险底线的重要工作,描述资产价格规律、准确度量尾部风险是风险管理的前提。为研究非对称性和非高斯性对我国股市收益率预测和尾部风险度量的影响,本文使用20种Levy-GARCH模型对上证综合指数进行实证分析,计算噪声服从跳跃过程时的VaR和CVaR值,结合快速傅里叶变换数值计算和回溯测试进行检验。研究结果表明:在中国股市中,非高斯性和非对称性是不可忽视的重要特征,跳跃行为在收益率拟合、预测和风险度量方面有重要影响;在尾部风险度量上,带跳跃的非仿射结构条件方差模型表现稳定地优于仿射结构模型,而且有限跳跃过程模型的综合表现优于带无限活动率跳跃过程的模型。总的来说,非对称、非高斯、非仿射的Levy-GARCH模型在收益率拟合与尾部风险测度上表现更好,而且有限跳跃形态可以更准确地解释中国股票市场的尾部风险。

Managing financial risk is crucial to guard against systematic risk,while risk management depends on describing stylized facts in stock markets and measuring tail risk.In Chinese stock market,we build 20 Levy-GARCH models to investigate the affect of asymmetry and non-Gaussianity on return prediction and tail risk measurement.We calculate the VaR and CVaR when noises follow jump processes and use fast Fourier transformation and back-testing in empirical research.According to empirical research on the Shanghai Stock Exchange Composite Index,asymmetry and non-Gaussianity are vital characteristics,and jump processes matter in fitting and predicting returns and measuring risks;in tail risk measurement,non-affine GARCH models with jumps outperform affine models,and GARCH models with finite intensity jump process perform better than those with infinite activity jumps.In conclusion,the non-affine Levy-GARCH models with asymmetry and non-Gaussianity perform well in return fitting and tail risk measurement,and jump process with finite intensity can explain tail risk in Chinese stock markets more precisely.