Abstract: 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.

Key words: ARCH models, nonparametric VaR, quantile regression, Monte Carlo simulation, local polynomial fitting