The Crude Oil Market Risk Measurement Based On The Garch-Stable Model

With the price of crude dropping, the market price of crude oil is attracting more and more attention. GARCH model is the most common method to measure the volatility. But a large number of studies show that the residuals of traditional GARCH still have obvious high peak and fat tail.That is, a basic assumption of the GARCH model:the iid assumption of the residuals, not establish, and the GARCH has a tendency to underestimate the risk. An approach to solve these problems is to use a thick tail distribution as the conditional distribution of GARCH model. In this paper, the stable distribution is used as the conditional distribution of the.In recent years, the fractal heat take stable distribution to public’s attention again. Stable distribution is a distribution with high peak and fat tail. By four parameters:feature parameter, kewness parameter, scale parameter and position parameter, it can adjust the tail, kurtosis, size, and skewness of the distribution flexibly. However, because its distribution function is not explicitly expressed, only through the numerical method can realize its value, and the development of computer technology has greatly promoted the application of stable distribution.This paper takes WTI and Brent, the two world’s largest crude oil varieties as an example to study the price risk of crude oil market. Firstly, we prove that the price of crude oil can be fitted with the stable distribution, and the fluctuation rate can be measured by the scale parameter of stable distribution. But the volatility is still at a static level. Then, stable distribution is used as the conditional distribution of GARCH model, so the concept of GARCH-stable model is put forward. And it is used to forecast the price fluctuation of crude oil market, and the use of stable distribution is extended to dynamic situation. In this paper, the maximum likelihood estimation method is used to estimate the parameters of GARCH-stable model, then the model’s conditional volatility is obtained. By using the graph test method, we find that the stable distribution fits the residual of the model very well, which effectively solves the problem that the residual of the GARCH model is not consistent with the conditional distribution.Further, this paper uses the most famous risk measurement method: VaR model to measure the risk of crude oil market. In order to compare the advantages and disadvantages of the model, the failure rate test of the VaR model is done under two confidence level:95% and 99%. The test results show that the GARCH-stable model is suitable. As a comparison, the GARCH-normal and other models, although the failure rate is in reasonable range by 95% confidence, but can’t pass the test under 99% confidence. As a supplement, the paper also introduced the fractal theory and some fractal analysis methods briefly, and introduced the stable distribution in detail.