参数VaR模型被广泛应用于风险测量中,然而需要给出具体的结构形式,这就容易发生模型错误设定的灾难,使风险计量的精确性易于产生较大偏差。针对参数VaR模型的设定误差问题,本文构建了SQ-ARCH和Nop-Quantile两个非参数VaR模型,诣在提高传统风险计量模型的灵活性、稳定性和准确性。采用稳健的分位数回归方法,得到了计算这两个VaR模型的具体表达式并给出了模型估计的算法和步骤。Monte Carlo模拟发现无论模型正确还是错误设定非参数VaR模型比参数ARCH类VaR模型更稳健。此外,把这两个稳健非参数VaR模型应用于我国股票市场风险量化的实证分析中。研究结果表明稳健非参数VaR模型比参数ARCH类VaR模型度量风险更准确。
The risk assessment is an important topic in risk management. The parametric VaR models are widely used in risk measurement. However, they are subject to large errors of model misspecification. In order to avoid the defect of parametric models, two nonparametric models for estimating VaR were proposed, which are SQ-ARCH and Nop-Quantile models. These two models are not restricted by their own specific structures and have great flexibility and stability in use. By the robust quantile regression method, we derived respectively the calculative steps and obtained the closed expressions of VaRs based on the two models. Monte Carlo simulation confirms that the nonparametric VaR models are more robust than the type of parametric ARCH VaR models, regardless of the correct or wrong setting of models. In addition, the two robust nonparametric VaR models are applied to qualify the risk of Chinese stock market by using the composite index data of Shanghai. It is founded that the returns of sample are non-normal and fat-tailed distribution. The technique of backtesting is used to examine the statistical properties of the nonparametric models and the ARCH models. The test results show that the robust nonparametric models outperform the type of non-robust parametric ARCH models in measuring VaR. The estimated risk values of ARCH are quite variable relative to the nonparametric models. Furthermore, the SQ-ARCH and Nop-Quantile models can yield more accurate VaR estimates than the ARCH models. The suggested models provided two effective methods for risk measurement.
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