基于Copula-EVT模型对股指在险价值的计量
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摘要
随着金融全球化进程的加快,金融市场面临的风险日益复杂化和多样化,有效的进行风险管理成为金融行业的重中之重。而风险管理的关键在于对风险价值的测量,如何精确的度量不同形式的风险成为学术界和金融界关注的热点和难点。本文搜集了全球主要的六支股指,从不同的投资决策出发,全而系统的运用不同的方法针对不同形式的资产价值估算风险价值。
本文有两条主线：一是资产形式,单一资产资产形式如沪深300,如果观察时变风险,本文采用基于GARCH类模型的参数估计法来估计其时变风险,如果投资者侧重于关注极值风险,本文运用极值理论来求其极值风险；对于资产组合形式,投资者或者投资机构不仅关注每项资产间的相关关系,还重视其相关模式,本文结合极值理论与Copula函数理论来求其在险价值。二是估计方法,本文按照从参数估计到半参数估计到非参数估计的思路对针对不同的投资决策来估计风险价值。看似是对风险测度方法的讨论,实则以研究方法为技术支撑来达到精确测度风险价值的目的。
大量的研究成果表明：金融时间序列收益率的分布呈现尖峰厚尾、波动的集聚性等特征,而不是传统假设的正态分布。针对这一特点本文的第三三章以讨论了沪深300的收益特征并在估算在险价值。本文采用偏态t分布下的FIGARCH模型来估计时变VaR。检验结果表明偏态t分布下的VaR估计优越于传统的正态分布、学生t分布、GED分布下的估计值。在金融风险的管理中,投资者往往更关注极值事件,所以如何合理的刻画极值分布,求出极值情况下的风险价值尤为重要。本文第四章利用极值理分别描述所搜集的六支股指的尾部分布情况并估计出VaR、CvaR。根据风险分散化原理,大多数投资者都会进行多元化的投资,以降低风险。这牵涉到多元极值的问题,第五章在极值理论的基础之上引入Copula函数理论,来简化多元极值问题。采用Copula-EVT模型分析由搜集到的六支股指等权重组成的资产组合的风险价值。失败率检验的结果表明：在95%和99%的显著性水平下,失败率和显著性水平都很接近,说明多元t-Copula模型能较好的描述多资产的相依性结构,Copula-EVT的模型选择适宜。
本文的最后对全文做了进行了总结,分析了本文研究的不足之处,在极值理论和Copula理论的研究现状之上对未来的研究方向做了展望。
The financial market is facing with increasingly complex and diversified risks, therefore, effective risk management has become a required course for the financial industry. The core of risk management is to measure the value at risk, so, how to accurately measure the risks in different forms become the focus of financial sector. In the paper, we collected six major world's stock index to measure different forms of asset's value according to different investment decisions.
A large number of research show that: the yields of financial series usually performance characteristics of the fat tail, volatility clustering, instead of the assumptions of normal distribution. In response to this, the third chapter discusses the CSI300yields' characteristics and estimate the value at risk. The CSI300yields performances not only a fat tail, volatility clustering, the fluctuations in the accumulation of such characteristics also showed obvious skewed distribution, as a result, we estimate time-varying VaRs based on FIGARCH model and choose skewed t distribution. The test results show that the estimation under skewed t distribution is superior to the traditional normal distribution, student's t distribution and the GED distribution. In risk management, once a small probability event such as the financial crisis occurs, the results will be extremely serious. So, how to accuratly describe extreme distribution and calculate the extreme value at risk is highly necessary. The fourth chapter describes the extreme distribution of A300, SH, HSI, the N225, ICIX,FCHI and estimate VaR, CVaR of them. In this process, the paper gives the fat-tail judgment, parameter estimation, the selection of the threshold, and the model estimation and testing methods, etc..The fifth chapter is to analysis value at risk of the portfolio based on Copula-the EVT model. Copula introduced into the extreme value theory to measure the risk is become one of the research frontier, Copula theory not only can separate the marginal distribution and the correlation structure of the random variable, but also can simplify complex issues. The Copula theory not only able to capture nonlinear asymmetric relationship between the variables, but also easy to capture the changes of variable tail. In recent years, there are lots of applications of copula function theory. But mainly in double circumstances, multivariate extreme value theory, especially introduce the Copula theory is seldom. The fifth chapter use Copula-EVT model to analyze the portfolio's VaR on the basis of the second chapter's theory and the third, fourth empirical analysis. Kupiec test results shows that:under the95%and99%significance level, the failure rate is close to the significance level, indicating that, the multivariate t-Copula model can describe dependency structure of multi-asset, Copula-EVT model is the appropriate choice.
The last is a summary of the paper, which analysis of the inadequacies of the paper, and put forward based on the present study of extreme value theory and Copula theory.
本文有两条主线：一是资产形式,单一资产资产形式如沪深300,如果观察时变风险,本文采用基于GARCH类模型的参数估计法来估计其时变风险,如果投资者侧重于关注极值风险,本文运用极值理论来求其极值风险；对于资产组合形式,投资者或者投资机构不仅关注每项资产间的相关关系,还重视其相关模式,本文结合极值理论与Copula函数理论来求其在险价值。二是估计方法,本文按照从参数估计到半参数估计到非参数估计的思路对针对不同的投资决策来估计风险价值。看似是对风险测度方法的讨论,实则以研究方法为技术支撑来达到精确测度风险价值的目的。
大量的研究成果表明：金融时间序列收益率的分布呈现尖峰厚尾、波动的集聚性等特征,而不是传统假设的正态分布。针对这一特点本文的第三三章以讨论了沪深300的收益特征并在估算在险价值。本文采用偏态t分布下的FIGARCH模型来估计时变VaR。检验结果表明偏态t分布下的VaR估计优越于传统的正态分布、学生t分布、GED分布下的估计值。在金融风险的管理中,投资者往往更关注极值事件,所以如何合理的刻画极值分布,求出极值情况下的风险价值尤为重要。本文第四章利用极值理分别描述所搜集的六支股指的尾部分布情况并估计出VaR、CvaR。根据风险分散化原理,大多数投资者都会进行多元化的投资,以降低风险。这牵涉到多元极值的问题,第五章在极值理论的基础之上引入Copula函数理论,来简化多元极值问题。采用Copula-EVT模型分析由搜集到的六支股指等权重组成的资产组合的风险价值。失败率检验的结果表明：在95%和99%的显著性水平下,失败率和显著性水平都很接近,说明多元t-Copula模型能较好的描述多资产的相依性结构,Copula-EVT的模型选择适宜。
本文的最后对全文做了进行了总结,分析了本文研究的不足之处,在极值理论和Copula理论的研究现状之上对未来的研究方向做了展望。
The financial market is facing with increasingly complex and diversified risks, therefore, effective risk management has become a required course for the financial industry. The core of risk management is to measure the value at risk, so, how to accurately measure the risks in different forms become the focus of financial sector. In the paper, we collected six major world's stock index to measure different forms of asset's value according to different investment decisions.
A large number of research show that: the yields of financial series usually performance characteristics of the fat tail, volatility clustering, instead of the assumptions of normal distribution. In response to this, the third chapter discusses the CSI300yields' characteristics and estimate the value at risk. The CSI300yields performances not only a fat tail, volatility clustering, the fluctuations in the accumulation of such characteristics also showed obvious skewed distribution, as a result, we estimate time-varying VaRs based on FIGARCH model and choose skewed t distribution. The test results show that the estimation under skewed t distribution is superior to the traditional normal distribution, student's t distribution and the GED distribution. In risk management, once a small probability event such as the financial crisis occurs, the results will be extremely serious. So, how to accuratly describe extreme distribution and calculate the extreme value at risk is highly necessary. The fourth chapter describes the extreme distribution of A300, SH, HSI, the N225, ICIX,FCHI and estimate VaR, CVaR of them. In this process, the paper gives the fat-tail judgment, parameter estimation, the selection of the threshold, and the model estimation and testing methods, etc..The fifth chapter is to analysis value at risk of the portfolio based on Copula-the EVT model. Copula introduced into the extreme value theory to measure the risk is become one of the research frontier, Copula theory not only can separate the marginal distribution and the correlation structure of the random variable, but also can simplify complex issues. The Copula theory not only able to capture nonlinear asymmetric relationship between the variables, but also easy to capture the changes of variable tail. In recent years, there are lots of applications of copula function theory. But mainly in double circumstances, multivariate extreme value theory, especially introduce the Copula theory is seldom. The fifth chapter use Copula-EVT model to analyze the portfolio's VaR on the basis of the second chapter's theory and the third, fourth empirical analysis. Kupiec test results shows that:under the95%and99%significance level, the failure rate is close to the significance level, indicating that, the multivariate t-Copula model can describe dependency structure of multi-asset, Copula-EVT model is the appropriate choice.
The last is a summary of the paper, which analysis of the inadequacies of the paper, and put forward based on the present study of extreme value theory and Copula theory.
引文
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