The Study, Based On Extreme Value Theory, Value At Risk (var) Model

Risk measurement is the basis of financial risk management. Now Value at Risk (VaR) is the mainstream method of financial risk management and a tool which is widely used. Traditional VaR methods want to give a hypothesis of financial return data subjected to some distribution, which can reduce the reliability of the model. However, the models of GEV and GPD, which are based on the theory of extreme value, just analyze the distribution of the tail in stead of the hypothesis. So it can avoid risk of model.This paper applies the GEV model and GPD model separately to carry on the analysis of real example to the risk in the futures market of nonferrous metals of our country and carries on the data analysis with R and EViews software. Through the analysis of real example, the paper draws a conclusion that the fitting result of GPD mode is obviously superior to that of GEV model. But at the same time, we find the absolute values of VaR which are calculated at 95% and 97.5% of the lower confidence level of GPD model are bigger. To this shortcoming of GPD model, the paper proposes a method to revise VaR of GPD model. This method regards the samples whose absolute value are less than or equal to threshold in the historical earning ratio array approximately as obeying normal distribution, the VaR calculated from the samples is written as VaR^*, and the VaR calculated in GPD model is written as VaR⁰. The revision method to VaR value that this paper puts forward gives VaR⁰ and VaR^* different weights separately under the same confidence level. Now we write the weights of VaR⁰ and VaR^* as w₀ and w_* respectively, which are such that w₀ and w_* are all greater than or equal to zero and no more than one and the summation of w₀ and w_* is one, then the VaR that has been revised is VaR = w₀VaR⁰ + w_*VaR^*. The advantage of this method lies in not only remedying the defect that much information contained in a lot of samples is lost while applying GPD model to calculate VaR, but also being enable investors to adjust two weights of VaR value according to one's risk partiality and prediction of the risk in the future and calculate the VaR that are more suitable to their own.In the end of the paper, we choose real earning ratio for three months of copper and aluminum futures of Shanghai futures exchange in our country as analytic target to carry on the analysis of real example and has proved the exactness of VaR revision method. This method can improve the accuracy for estimating VaR value and has important reference value and directive significance to financial institutions and individual investors employing VaR to control the market risk.