基于GARCH族和EVT模型的股市风险价值的比较研究
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摘要
随着经济全球化及投资自由化的日益加剧,金融市场风险导致各金融机构之间的竞争从原来的资源竞争逐渐转变为内部管理、业务创新、企业文化等方面的竞争,金融机构的风险管理成为现代金融企业管理基础和发展的基石。在这样的背景下,国外各金融机构格外注重金融风险的测定和管理。如何构建合适的模型以恰当的方法对风险进行测量是当前金融研究领域的一个热门话题。VaR方法作为当前业内比较流行的测量金融风险的方法,具有简洁、明了的特点,而在研究金融市场波动方面,GARCH族模型是一类极受欢迎的非线形金融时间序列模型。
本文在对股市金融时间序列分布性质进行系统分析的基础上,运用VaR方法,用当前金融领域刻画条件方差最典型的GARCH模型及其几种最新衍生模型如EGARCH、PARCH等对两种风险值VaR和CVaR进行了研究,并利用上证指数1997.1.2-2008.5.23的数据,实证研究了股市的市场风险。论文主要结论包括:(1)分析上证综指对数日收益序列的统计特征,证明序列的分布具有尖峰厚尾的特征,并呈现出群集性效应和持久性;市场存在明显的杠杆效应,波动存在明显的非对称性,并且负的冲击带来的波动大于正冲击。(2)分别在正态分布、t-分布以及GED分布假设下建立GARCH模型族的动态风险价值的度量模型,证明在t-分布、GED分布对序列尾部特征的刻画明显优于正态分布,能刻画出收益厚尾的分布特征,并且EGARCH模型能捕捉股市的杠杆效应,即对正负干扰的不对称性,能更准确刻画股票的波动性,有优于GARCH模型的风险度量结果。(3)根据EVT模型也适合刻画资产收益的厚尾分布,选用POT方法建模,得到了另一种基于GARCH族模型和极值理论的VaR/CVaR有效动态风险度量方法,并利用Kupiec提出的LR统计量检验法对模型的结果进行了分析比较,证明在这种方法下,对上证股指风险的预测更为准确。(4)通过上证指数的实证分析,提出了相关政策建议。
The risk of financial market resulted in the resource competition among various financial institutions to gradually translate into the competition in inner management、operation innovation and corporation cultures, along with the economy worldwise and increasingly prick up in investment open. The situations make the risk management in financial institutions become the foundation of management and development in modern finance corporations. The management of financial market risk increasingly stands out, how to determine and control market risk becomes the issure anxious to solve in financial securities institution、investor and correlative supervisor organization. Under the background, various overseas financial institutions excessive pay attention to the determine and control about the risk. How to design the appropriate models and use the suitable measures to measure risk turn into a pop topic in finance research domanial. Value-at-Risk is a more popular method used to measure risk, which has the characteristic of concision and perspicuous, At the aspect of researching the market volatility, GARCH model and its many relatives are well used for non-linear financial time series.
In the paper, we give a systems analysis to the distributing characters of financial time series in stock market. After that, we study the VaR and conditional VaR with the Value-at-Risk method, using the most typical GARCH model and its many relatives including EGARCH、PARCH models and so on to depict conditional variance in finance domain. Besides, we compute the VaR and CVaR about shanghai stock index, using its practical data from January 2, 1997 to May 23, 2008. The paper contains following studies and results: (1) we analyse the statistical characteristics of the log-return rate sequence about shanghai stock index, then we prove that the sequence have the characteristics: fat tails and sharp kurtosis of return distribution and dynamic volatility resulting in the phenomenon of volatility clustering and persistence; there is leverage effect in the market and remarkable asymmetry effect in volatility. We also know the negative shock give a more volatility than the positive one. (2) We get the methodology of VaR and conditional VaR based on the GARCH and EGARCH models with various distributions (include,normal,Student-t and GED) and hence modify the methodology of VaR and CVaR. The outcome tell us that the fat tail of return sequence can be better described with the GED and Student-t distributions than with the normal distribution. In addition, EGARCH model is able to capture the leverage effect in stock market, correspondence specking, it is asymmetric to the effect of negative shock and positive shock, which is more accurately to describe the stock volatility and we get a better outcome based EGARCH model than GARCH model. (3) While the application of Extreme Value Theory is relatively congruent in tracking the fat tails of asset return distribution, we choose the POT method, and the phenomenon of volatility clustering has been extensively studied using GARCH model and its many relatives. The paper combines the two methodologies to come up with a robust dynamic risk management method: GARCH,etc-EVT-VaR/CVaR. Further we analyse and compare the outcome of each model based on Kupiec LR failure rate test. We get the method of GARCH,etc-EVT can more accurately forecast the risk in stock market. (4) At last, we put forward some relevant polices on the basis of the demonstration study about the models we get in the front chapters.
本文在对股市金融时间序列分布性质进行系统分析的基础上,运用VaR方法,用当前金融领域刻画条件方差最典型的GARCH模型及其几种最新衍生模型如EGARCH、PARCH等对两种风险值VaR和CVaR进行了研究,并利用上证指数1997.1.2-2008.5.23的数据,实证研究了股市的市场风险。论文主要结论包括:(1)分析上证综指对数日收益序列的统计特征,证明序列的分布具有尖峰厚尾的特征,并呈现出群集性效应和持久性;市场存在明显的杠杆效应,波动存在明显的非对称性,并且负的冲击带来的波动大于正冲击。(2)分别在正态分布、t-分布以及GED分布假设下建立GARCH模型族的动态风险价值的度量模型,证明在t-分布、GED分布对序列尾部特征的刻画明显优于正态分布,能刻画出收益厚尾的分布特征,并且EGARCH模型能捕捉股市的杠杆效应,即对正负干扰的不对称性,能更准确刻画股票的波动性,有优于GARCH模型的风险度量结果。(3)根据EVT模型也适合刻画资产收益的厚尾分布,选用POT方法建模,得到了另一种基于GARCH族模型和极值理论的VaR/CVaR有效动态风险度量方法,并利用Kupiec提出的LR统计量检验法对模型的结果进行了分析比较,证明在这种方法下,对上证股指风险的预测更为准确。(4)通过上证指数的实证分析,提出了相关政策建议。
The risk of financial market resulted in the resource competition among various financial institutions to gradually translate into the competition in inner management、operation innovation and corporation cultures, along with the economy worldwise and increasingly prick up in investment open. The situations make the risk management in financial institutions become the foundation of management and development in modern finance corporations. The management of financial market risk increasingly stands out, how to determine and control market risk becomes the issure anxious to solve in financial securities institution、investor and correlative supervisor organization. Under the background, various overseas financial institutions excessive pay attention to the determine and control about the risk. How to design the appropriate models and use the suitable measures to measure risk turn into a pop topic in finance research domanial. Value-at-Risk is a more popular method used to measure risk, which has the characteristic of concision and perspicuous, At the aspect of researching the market volatility, GARCH model and its many relatives are well used for non-linear financial time series.
In the paper, we give a systems analysis to the distributing characters of financial time series in stock market. After that, we study the VaR and conditional VaR with the Value-at-Risk method, using the most typical GARCH model and its many relatives including EGARCH、PARCH models and so on to depict conditional variance in finance domain. Besides, we compute the VaR and CVaR about shanghai stock index, using its practical data from January 2, 1997 to May 23, 2008. The paper contains following studies and results: (1) we analyse the statistical characteristics of the log-return rate sequence about shanghai stock index, then we prove that the sequence have the characteristics: fat tails and sharp kurtosis of return distribution and dynamic volatility resulting in the phenomenon of volatility clustering and persistence; there is leverage effect in the market and remarkable asymmetry effect in volatility. We also know the negative shock give a more volatility than the positive one. (2) We get the methodology of VaR and conditional VaR based on the GARCH and EGARCH models with various distributions (include,normal,Student-t and GED) and hence modify the methodology of VaR and CVaR. The outcome tell us that the fat tail of return sequence can be better described with the GED and Student-t distributions than with the normal distribution. In addition, EGARCH model is able to capture the leverage effect in stock market, correspondence specking, it is asymmetric to the effect of negative shock and positive shock, which is more accurately to describe the stock volatility and we get a better outcome based EGARCH model than GARCH model. (3) While the application of Extreme Value Theory is relatively congruent in tracking the fat tails of asset return distribution, we choose the POT method, and the phenomenon of volatility clustering has been extensively studied using GARCH model and its many relatives. The paper combines the two methodologies to come up with a robust dynamic risk management method: GARCH,etc-EVT-VaR/CVaR. Further we analyse and compare the outcome of each model based on Kupiec LR failure rate test. We get the method of GARCH,etc-EVT can more accurately forecast the risk in stock market. (4) At last, we put forward some relevant polices on the basis of the demonstration study about the models we get in the front chapters.
引文
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杜海涛. 2000. VaR模型在证券风险管理中的应用[J].证券市场导报,8:57-61.
范英. 2001.股市风险值估计的EWMA方法及其应用[J].预测Forecasting, 3(20):34-37.
龚锐,陈仲常,杨栋锐. 2005. GARCH族模型计算中国股市在险价值风险的比较研究与评述[J].数量经济技术经济研究, 7:67-81.
胡援成,姜光明. 2004.上证综指收益波动性及VaR度量研究[J].当代财经, 6:34-38.
霍玉琳,何春雄. 2006. GARCH模型下的极值一致风险度量[J]. Finance&Economy,2:152-154.
李聪.运用GARCH族模型在不同分布下对深证综指的VaR分析[J].统计观察, 9:79-80.
李华中,杨湘豫. 2002.中国证券市场股指波动的条件异方差特性分析[J].经济数学, 6:37-43.
李亚静,朱宏泉. 2000.基于VaR的风险分析理论与计算方法[J ] .预测,5(19):36 -39.
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