基于GARCH-stable模型的原油市場風險度量
發(fā)布時間：2019-01-13 10:28
【摘要】：隨著原油價格的暴跌,原油的市場價格風險越來越受到人們的關(guān)注。對波動率的衡量最常用的方法是GARCH模型。但是大量的研究表明傳統(tǒng)的GARCH的殘差仍然存在明顯的尖峰厚尾性,也就是說GARCH模型的一個基本假設：殘差服從獨立同分布標準正態(tài)分布,是不成立的；而且GARCH有低估風險的傾向,模型風險不容忽視。解決這些問題的一個辦法是用某個厚尾分布作為GARCH模型的條件分布。本文采用stable分布作為其條件分布。近年來的分形熱讓stable分布重新受到關(guān)注,stable分布是一種具有尖峰厚尾性的分布,通過四個參數(shù)：特征指數(shù)、偏斜指數(shù)、尺度參數(shù)和位置參數(shù),可以靈活的調(diào)節(jié)分布的尾部、峰度、尺寸,甚至偏斜度。但是由于它的分布函數(shù)不存在顯式的表達式,只有通過數(shù)值法才能實現(xiàn)其價值,計算機技術(shù)的發(fā)展極大的促進了stable分布的應用。本文以WTI和Brent兩個世界上最大的原油品種為例,研究原油市場的價格風險。首先證明了原油價格變化可以用獨立同分布stable分布擬合,這時價格波動率能夠用stable分布的尺度參數(shù)σ度量,但是這里的波動率停留在靜態(tài)的層次上,不具有時變性。然后本文將stable分布作為GARCH模型的條件分布,提出了GARCH-stable模型的概念,并用來預測原油市場的價格波動率,把stable分布的使用擴展到了動態(tài)的情形。本文使用極大似然估計法作GARCH-stable模型的參數(shù)估計,得到了模型的條件波動率σt,并且采用圖檢驗法對模型的殘差進行檢驗,發(fā)現(xiàn)stable分布對模型殘差的擬合度很高,有效地解決了GARCH模型的殘差與條件分布不吻合的問題,用它作為GARCH模型的條件分布非常合適。進一步地,本文在前面得到的條件波動率σt的基礎(chǔ)上,采用最著名的風險度量方法--VaR模型,度量原油市場風險。為了對比模型的優(yōu)劣,本文對VaR模型做了失敗率檢驗。95%和99%兩個置信度下的檢驗結(jié)果表明了GARCH-stable模型是合適的,相比之下,GARCH-normal等模型雖然通過了95%置信度下的失敗率檢驗,但是卻沒有通過卻沒有通過99%置信度下單失敗率檢驗。作為補充,本文還簡要介紹了分形理論與分形分析方法,并對stable分布做了具體的介紹。
[Abstract]:With the collapse of crude oil price, people pay more and more attention to the market price risk of crude oil. The most commonly used method for measuring volatility is the GARCH model. But a large number of studies show that the residual of traditional GARCH still has obvious spike and thick tail, that is to say, a basic assumption of GARCH model: the standard normal distribution of residual clothing from independent same distribution, is not true; And GARCH has the tendency to underestimate the risk, model risk can not be ignored. One way to solve these problems is to use a thick tail distribution as the conditional distribution of the GARCH model. In this paper, stable distribution is used as its conditional distribution. The fractal heat in recent years has refocused the stable distribution. The stable distribution is a kind of distribution with sharp peak and thick tail. It can adjust the tail of the distribution flexibly through four parameters: characteristic index, skew index, scale parameter and position parameter. Kurtosis, size, even skew. However, because its distribution function does not have explicit expression, it can realize its value only by numerical method. The development of computer technology has greatly promoted the application of stable distribution. This paper takes WTI and Brent as examples to study the price risk of crude oil market. Firstly, it is proved that the price change of crude oil can be fitted by independent and distributed stable distribution, and the price volatility can be measured by the scale parameter 蟽 of the stable distribution, but the volatility stays at the static level and does not have time variability. Then, the stable distribution is taken as the conditional distribution of the GARCH model, and the concept of GARCH-stable model is put forward, which is used to predict the price volatility of crude oil market, and the use of stable distribution is extended to the dynamic case. In this paper, the maximum likelihood estimation method is used to estimate the parameters of the GARCH-stable model. The conditional volatility 蟽 t of the model is obtained, and the residual error of the model is tested by the graph test method. It is found that the stable distribution has a high fitting degree to the model residual. The problem that the residual error of GARCH model is not consistent with the conditional distribution is effectively solved, and it is very suitable to use it as the conditional distribution of GARCH model. Furthermore, on the basis of the conditional volatility 蟽 t, this paper uses the most famous risk measurement method, VaR model, to measure the market risk of crude oil. In order to compare the advantages and disadvantages of the model, the failure rate of the VaR model is tested. The test results under 95% and 99% confidence level show that the GARCH-stable model is suitable. Although GARCH-normal and other models pass the 95% confidence test, they fail to pass the 99% confidence test. As a supplement, fractal theory and fractal analysis method are briefly introduced, and stable distribution is introduced in detail.
【學位授予單位】：浙江工商大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：F416.22
本文編號：2408348
[Abstract]:With the collapse of crude oil price, people pay more and more attention to the market price risk of crude oil. The most commonly used method for measuring volatility is the GARCH model. But a large number of studies show that the residual of traditional GARCH still has obvious spike and thick tail, that is to say, a basic assumption of GARCH model: the standard normal distribution of residual clothing from independent same distribution, is not true; And GARCH has the tendency to underestimate the risk, model risk can not be ignored. One way to solve these problems is to use a thick tail distribution as the conditional distribution of the GARCH model. In this paper, stable distribution is used as its conditional distribution. The fractal heat in recent years has refocused the stable distribution. The stable distribution is a kind of distribution with sharp peak and thick tail. It can adjust the tail of the distribution flexibly through four parameters: characteristic index, skew index, scale parameter and position parameter. Kurtosis, size, even skew. However, because its distribution function does not have explicit expression, it can realize its value only by numerical method. The development of computer technology has greatly promoted the application of stable distribution. This paper takes WTI and Brent as examples to study the price risk of crude oil market. Firstly, it is proved that the price change of crude oil can be fitted by independent and distributed stable distribution, and the price volatility can be measured by the scale parameter 蟽 of the stable distribution, but the volatility stays at the static level and does not have time variability. Then, the stable distribution is taken as the conditional distribution of the GARCH model, and the concept of GARCH-stable model is put forward, which is used to predict the price volatility of crude oil market, and the use of stable distribution is extended to the dynamic case. In this paper, the maximum likelihood estimation method is used to estimate the parameters of the GARCH-stable model. The conditional volatility 蟽 t of the model is obtained, and the residual error of the model is tested by the graph test method. It is found that the stable distribution has a high fitting degree to the model residual. The problem that the residual error of GARCH model is not consistent with the conditional distribution is effectively solved, and it is very suitable to use it as the conditional distribution of GARCH model. Furthermore, on the basis of the conditional volatility 蟽 t, this paper uses the most famous risk measurement method, VaR model, to measure the market risk of crude oil. In order to compare the advantages and disadvantages of the model, the failure rate of the VaR model is tested. The test results under 95% and 99% confidence level show that the GARCH-stable model is suitable. Although GARCH-normal and other models pass the 95% confidence test, they fail to pass the 99% confidence test. As a supplement, fractal theory and fractal analysis method are briefly introduced, and stable distribution is introduced in detail.
【學位授予單位】：浙江工商大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：F416.22
【共引文獻】
相關(guān)期刊論文 前1條
1 伍笑萍;李忠民;;基于GARCH模型的WTI原油現(xiàn)貨市場的風險分析[J];合肥工業(yè)大學學報(自然科學版);2013年09期
相關(guān)博士學位論文 前1條
1 陳磊;石油市場的內(nèi)外部聯(lián)系、價格發(fā)現(xiàn)與風險管理研究[D];電子科技大學;2012年
，本文編號：2408348
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