Bootstrap Prediction Intervals For Value At Risk And Expected Shortfall For Metal Futures Market

Our country is a developing country, a variety of raw materials, especially metal, are in huge demand. Metal prices are vulnerable to the influence of various factors, which is often violent fluctuation. And the metal prices’ volatility can not only make relevant enterprises difficult to business but also not be conducive to the steady development of national econo-my. In this situation, to accurately measure the risk of metal futures market in China has important practical significance.This paper propose a Bootstrap procedure and obtain prediction intervals of future Value at Risk and Expected Shortfall in the context of univariate GARCH models. We use the simulation analysis to compare the sliding window method and normal distribution model to build risk measure VaR and ES the prediction precision of confidence interval with the Bootstrap method. The simulation results show that the Bootstrap method to build the confidence interval of risk measure VaR and ES have the highest prediction accuracy. The rationality of the method presented in this paper. In the empirical analysis part, the metal futures market risk measure VaR and ES prediction interval problem is to do the research based on the Shanghai futures exchange copper and aluminum, which are two kinds of index futures as the object of empirical analysis. First of all, we do with descriptive statistics for Shanghai copper and aluminum yield sequences.We found that Shanghai copper and aluminum showed obvious peak gathered and thick tail.Second, the different GARCH model is used to calculate VaR and ES of Shanghai aluminum and copper. The empirical results show that GARCH-t model has the highest precision for Shanghai copper index and GJRGARCH-t model has the highest accuracy for Shanghai aluminum index. Finally, this paper establish the forecast interval of VaR and ES based on the Bootstrap method and GARCH model for Shanghai aluminum and copper index. From the band width this perspective, the VaR and ES width of confidence interval is the smallest based on the Bootstrap method and GARCH-1 model for the Shanghai copper index. The VaR and ES width of confidence interval is the smallest based on the Bootstrap method and GJRGARCH-t model for the Shanghai aluminum index. This shows that the method to establish the risk measure of the confidence interval of VaR and ES have the highest accuracy.Although the methods of this paper can enrich the existing risk management theory, we find that the future research is to deal with some of the following question. This paper establish the forecast interval of risk measure VaR and ES based on the residual Bootstrap method and GARCH model, which don’t compare the prediction interval with other Bootstrap method. We also don’t compare the residual Bootstrap method and GARCH model with the residual Bootstrap method and other types of volatility models (e.g., SV model). All of these will be our future research direction.