The Commodity Futures' VaR Measurement Research Based On Extreme Value Theory

With the development of China's futures market, the futures' trading is expanding fast. It's showed that, the proportion of the total trading in Zhengzhou, Shanghai and Dalian to the volume of whole world is 48.7% according to the first half of 2010 statistical results of FIA. Therefore, how to measure the risk accurately in the process of commodity futures trading has become an important problem. In this situation, this paper used the method which combined GARCH model with extreme value theory (EVT) to measure the dynamic risk value (VaR).This paper made an empirical analysis of Zhengzhou cotton index, Shanghai copper index and Dalian soybean index. Firstly, I filtered that logarithmic return series by GARCH model and processed their correlation and heteroskedasticity, and got the conditional variances as well as standardized residual sequence. This paper mainly discussed the modeling which was used to analyze the cotton index based on extreme value theory. Furthermore, there were three different methods of GARCH-N, GARCH-t and GARCH-EVT which were used to do modeling contrast analysis for various futures in three different conditional distribution assumptions. Meanwhile, I drew the percentile level under various distribution models and estimated dynamic VaR in the paper. What's more, the paper compared dynamic VaR results of cotton index with each other which estimated by four models GARCH-EVT, GARCH-M-EVT, GJR-EVT and GJR-M-EVT. Finally, the paper took Backtesting for dynamic VaR series which were estimated by various models.Being different from most domestic existing empirical findings, the empirical of the paper results indicated that the conditional distribution of cotton index was in line with thin tail rather than fat tail. Dynamic VaR which was estimated by GARCH-N and GARCH-t failed to pass Backtesting, but GARCH-EVT model based on the extreme distribution obtained significantly better VaR measurement accuracy. GARCH-EVT, GARCH-M-EVT, GJR-EVT and GJR-M-EVT which were used to measure dynamic VaR results of cotton index all passed Backtesting. However, there were not obvious differences among them. Meanwhile, results of three commodity indexes proved that EVT was stable for dynamic VaR estimation of commodity futures.