基于Copula模型下的VaR度量及其应用

发布时间：2018-03-23 07:40

本文选题：Kendall　切入点：tau　出处：《西南交通大学》2013年硕士论文　论文类型：学位论文

【摘要】：金融产品的多样化,金融市场的不稳定性等原因导致金融资产风险的不可控,因此研究风险价值具有很广很深的实际意义。多资产组合风险因金融市场的灵活多样,故其关键问题是动态相依机制的刻画,而时变Copula函数能够很好的刻画变量间的相依机制。本文根据金融市场特征以及Copula建模理论,从Copula所导致的相依指标Kendall tau尾相关系数出发,将构造方法和建模技术结合在一起,建立了时变Copula模型,成功描述了非线性的、非正态的时变相依机制,成功捕捉了下尾相依机制的时变性。主要工作包括： (1)从模式的识别、模型的检验等方面分析了阿基米德Copula模型的优良性质,并结合金融数据的特性,说明了利用时变阿基米德Copula模型分析风险的可行性、有效性、优越性。 (2)本文从阿基米德Copula函数与Kendall tau、尾相关系数之间的一一对应关系出发,建立基于时变Kendall tau、时变尾相关系数的阿基米德Copula模型。 (3)假定Clayton Copula的时变参数为非线性的AR(1)模型,从Kendall tau和尾相关系数两个角度出发,分别建立时变Copula模型,结合蒙特卡洛模拟技术和拟合优度检验,最终说明了从Kendall tau角度建立的时变Copula模型要优于尾相关,基于Kendall tau的时变阿基米德Copula模型更能捕捉非线性的、非正态的时变相依机制,具有一定的优越性。 (4)针对沪深股市的波动性以及非正态分布的非线性相依机制,结合Copula构造方法和建模技术,以t-Garch模型描述了沪深指数收益率的边缘分布,采用拟合优度检验选取最佳的Clayton Copula模型。 (5)根据建立的边缘分布模型,并结合Clayton Copula模型,分别建立了单参数静态Clayton Copula和时变Clayton Copula模型,计算对数收益率所对应的VaR值。 (6)将双参数时变BB1Copula与风险价值相结合,建立双参数时变Copula模型度量VaR,并对比了时变双参数Copula模型与时变单参数Copula模型和传统Copula模型在度量多资产组合风险的优劣。
[Abstract]:The diversification of financial products, financial market instability and other reasons lead to the risk of financial assets is not controllable, with a very wide deep practical significance. Therefore research on risk value of portfolio risk due to the financial market is flexible, so it is the key problem of dynamic dependent mechanism, and time-varying Copula function can be dependent mechanism the variables in this paper. According to the characteristics of the financial market and the Copula modeling theory, starting from Copula to the Kendall tau dependent index tail correlation coefficient, the construction method and modeling technology together, build the time-varying Copula model successfully described, nonlinear, non normal time-varying dependent mechanism. Capture time-varying dependent mechanism including the tail:
(1) from the aspects of pattern recognition and model checking, we analyze the fine properties of Archimedes Copula model. Combined with the characteristics of financial data, we illustrate the feasibility, effectiveness and superiority of using time-varying Archimedes Copula model to analyze risks.
(2) starting from the one-to-one correspondence between Archimedes's Copula function and Kendall tau and tail correlation coefficient, we establish a Archimedes Copula model based on time-varying Kendall tau and time-varying tail correlation coefficient.
(3) Clayton Copula assumes that time-varying parameters for nonlinear AR (1) model, starting from the two angles of Kendall tau and the tail correlation coefficient, respectively establish time-varying Copula model. Combining with Monte Carlo simulation and test of goodness of fit, the establishment of the tau from the Kendall point of the time-varying Copula model is better than the tail, based on Kendall tau time-varying Archimedes Copula model can capture the nonlinear, non normal time-varying dependent mechanism, has certain advantages.
(4) in view of the volatility and non normal distribution mechanism of the Shanghai and Shenzhen stock markets, combined with the Copula construction method and modeling technology, we describe the marginal distribution of the Shanghai and Shenzhen stock index returns based on the t-Garch model, and select the best Clayton Copula model by goodness of fit test.
(5) according to the established edge distribution model and Clayton Copula model, single parameter static Clayton Copula and time-varying Clayton Copula models are established respectively, and the VaR value corresponding to logarithmic yield is calculated.
(6) combining the two parameter time-varying BB1Copula and the value at risk, we establish a two parameter time-varying Copula model to measure VaR. We compare the time varying two parameter Copula model with the time-varying single parameter Copula model and the traditional Copula model to measure the risk of multiple asset portfolios.

【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.91

【参考文献】