【作者】 马艳民；

【导师】 吴润衡；

【作者基本信息】 北方工业大学 ， 应用数学， 2008， 硕士

【摘要】 金融风险的研究动因是由于隐含风险因子在许多未知变化下而导致的金融资产的损失或收益。金融机构的发展受到许多风险情况的限制。为了更好的预测和控制风险,研究者和金融机构设计了许多度量风险的方法,其中VaR方法是最常采用的方法。但是基于假定单个资产收益正态,风险资产间收益线性相关计算VaR与实际情况并不相符。Copula理论的出现和应用为将风险分析和多变量时间序列分析提供了一个新的方向。用Copula来刻画金融市场间的相关结构,不仅可以选择更好的描述风险资产收益的分布函数,还可以将金融市场间的相关结构剥离出来,更全面地刻画风险资产间的相依程度。本文介绍了Copula理论,因单一Copula函数并不能全面的描述金融市场复杂多变的情况,给出了更适合描述股市风险资产的具有时变性和变结构的Copula模型。利用上证指数、深证综指日收益率数据(2001年9月11日至2007年11月30日)对混合Copula模型和单一的Copula族模型应用于VaR的计算作了实证分析,结果表明混合Copula在估算VaR/CVaR的精度方面优于仅基于单一Copula函数的估算方法。尾部相关性可以较好地描述极端事件出现时资产间的相互作用。以往实证研究表明,通常情况下,尾部相关性在市场大幅下跌期较强,而在市场上涨期较弱。因此尾部相依关系的研究对了解、控制股市出现重大风险非常重要。本文对此也进行了比较系统的阐述,并且给出了具有较强尾部相依关系的变结构Copula模型。更多还原

【Abstract】 The motivation of financial risk is the loss or gain of the financial assets caused by many uncertainties changes for an implied risk factor. The development of financial institutions is subject to many risks in the restrictions. In order to better predict and control the risk, the researchers and financial institutions design a number of risk measurement methods, in which VaR is used most often. However, based on the assumption that the gains of a single capital are normal, the income linear dependent calculation of VaR in the risk assets does not match the actual situation. The emergence and application of Copula theory for risk analysis and multivariable time series analysis provide a new direction. Copula is used to describe the correlation in financial market structure, not only can choose a better description of the gains of risk capital distribution function, but also can strip out the correlation in financial market structure, more fully describe the level of dependencies in the risk assets.In this paper, Copula theory is introduced. Because single Copula function can not describe the complex and volatile financial markets comprehensively, we give more suitable Copula model with variability and change structure, which describe the risk assets of stock market. Using Shanghai Stock Index and Shenzhen Composite Stock Index (September 11, 2001 to November 30, 2007) ,we make a empirical analysis about mixed Copula model and a single model applying the VaR calculation. The result show that mixed Copula is better than a single Copula group to simulate the dependence of the risk assets.Tail dependence can be used to describe interaction in assets when the extreme events arise. The past empirical studies show that, under the normal circumstances, the tail dependence is stronger in the declined substantially period of the market, but in the period of rising market, it is weaker. Therefore the research of the tail dependence is very important to understand and control of the major risk of the stock market. This paper also makes a more systematic exposition, and gives a variable structure Copula model with a stronger tail dependence.更多还原