基于t-Copula下信用资产组合的综合风险度量及实证研究

发布时间：2018-02-21 02:42

本文关键词： 结构模型 Copula函数异质资产组合重要抽样技术 ES　出处：《浙江财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：对信用资产组合的风险度量研究一直以来都是学者关注的重点，基本模型主要分为结构模型、简约模型。这些模型的最终意图都是发展出一套科学系统的体系来度量风险，以求合理定价或防范未来可能发生的损失。而对于组合的相关性结构以及组合风险计算的复杂性却鲜有研究，直到2008年金融危机的爆发，由于尾部风险的忽略而导致的违约事件急剧增加才引起了学者们对于组合风险的相关结构的研究。为此，本文研究一种能够刻画异质性信用资产组合尾部相关性的有效度量风险的方法，并对上市股票相关数据做实证分析。首先，本文概括性介绍了模型的理论基础。主要介绍了结构模型的定义，阐述结构模型的基本思想和推导的相关衍生模型。同时详细阐述了组合相关性结构选取所采用的Copula系函数的定义、类别、对应参数估计方式以及所推导的各类相关系数定义公式。其次，本文针对组合的相关性结构进行了详细的研究。针对传统的组合之间采用正态Copula模型构建相关性，本文采用了t-Copula模型来构建并考虑了组合之间的尾部相关关系，以更好准确的测量风险值。与此同时，本文将资产组合同质的限制扩展到了异质组合的条件之下，刻画组合之间的非线性相关关系，其所得结果更加贴近现实。然后，本文研究了Copula模型下重要抽样技术。普通蒙特卡罗模拟在组合样本数量急剧增加下模拟时间将会大大延长，，国内外对于统计学中的重要抽样技术的研究较多，而应用于组合风险中的研究却较少，尤其是基于Copula函数的基础之上的相关研究。本文介绍了正态Copula下组合风险值计算方法，在此基础上研究了t-Copula下重要抽样技术的风险值计算公式。对于传统中的重要抽样技术均值漂移项所采用的高斯牛顿法，本文引入了同时兼有梯度法和牛顿法更加智能的Levenberg-Marquardt算法。通过数值模拟比较了正态Copula和t-Copula两模型的重要抽样下的蒙特卡罗模拟的有效性，发现重要抽样技术的确能更加快速有效的测量风险值。最后，本文选取上交所中房地产、零售业、金融保险业的上市股票相关数据做实证分析。通过Black-Scholes Merton模型的求解得到了结构模型所需要的每支股票的时刻公司资产价值以及标准收益率，通过核密度估计得到每支股票的边际分布。利用t-Copula系函数以及非线性估计我们分别得到了组合的相关结构以及异质资产组合的各因子系数，进而得到了组合的整体违约概率。结合重要抽样技术，我们计算得到了组合的风险VaR值和ES值，结果表明重要抽样技术在保证精确度的前提下的确减少了抽样的方差，同时引入ES值可以更好的进行风险监管。综上所述，本文考虑异质性组合的非线性相关关系，通过t-Copula系函数构造组合之间的相关关系能更准确的刻画组合的违约概率，同时结合重要抽样技术可以更加有效的测算组合的风险VaR和ES值，为极端事件的研究以及投资者配置经济资本和监管者进行风险监管提供了依据。
[Abstract]:The research on the risk measurement of the portfolio of credit assets has always been the focus of scholars ' attention . The basic model is mainly divided into structural model and simplified model . The final intention of these models is to develop a system of scientific system to measure the risk , so as to reasonably price or guard against possible losses in the future . Firstly , the theory basis of the model is introduced in this paper . The definition of the structural model is introduced , the basic idea of the structural model and the related derivative model are described . At the same time , the definition , the category , the corresponding parameter estimation method and the deduced formula of the correlation coefficient are described in detail . Secondly , this paper studies the correlation structure of the combination . In this paper , we use the t - Copula model to construct the correlation . In the meantime , we use the t - Copula model to construct and take into account the tail correlation between the combinations to better measure the risk value . At the same time , this paper extends the restriction of the homogeneity of the portfolio to the non - linear correlation between the heterogeneous combination , and the result is closer to the reality . In this paper , we have studied the important sampling technique under the Copula model . The simulation time will be greatly prolonged under the sharp increase of the number of combined samples , but the research on the important sampling technique in the statistics is less , especially on the basis of Copula function . The paper introduces the Levenberg - Marquardt algorithm which is more intelligent than Newton method . Finally , this paper analyzes the relevant data of the listed stock of real estate , retail and financial insurance in Shanghai Stock Exchange . By using the Black - Black Merton model , we obtain the asset value and standard rate of return of each stock . By using t - Copula system function and nonlinear estimation we get the combined risk VaR and ES value respectively . The results show that the important sampling technique can reduce the variance of sample by using t - Copula system function and nonlinear estimation . The results show that the important sampling technique can reduce the variance of sample under the premise of guaranteeing accuracy , while introducing ES value can better carry out risk supervision . In conclusion , this paper considers the non - linear correlation of heterogeneous combination , the correlation between t - Copula system function is more accurate , and the combination risk VaR and ES value can be measured more effectively by combining the important sampling technique , which provides the basis for the research of extreme events and the risk supervision of investors ' allocation of economic capital and regulators .

【学位授予单位】：浙江财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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