基于混合Copula篮式信用违约互换定价研究

发布时间：2018-06-23 14:36

本文选题：信用衍生品 + 篮式信用违约互换　；参考：《大连理工大学》2013年硕士论文

【摘要】：信用违约互换是金融机构进行信用风险管理的表外工具,是信用衍生品种交易量最大的产品。信用违约互换定价模型也成为了国内外学者研究的焦点。2010年中国版信用违约互换-信用风险缓释工具(CRM)推出以来发展缓慢,定价模型的不完善成为CRM市场可持续发展的瓶颈之一。篮式信用违约互换将多项资产作为一个组合进行风险管理操作,能够有效降低风险管理成本以及交易成本,有利于提高资产组合风险管理水平,成为近期衍生品市场发展最快的信用衍生品之一。本文利用混合Copula函数拟合违约时间的联合分布,并将混合Copula函数引入篮式信用违约互换定价公式,建立基于混合Copula的篮式信用违约互换定价模型,为篮式信用违约互换定价提供方法和工具。本文的主要工作： (1)构建混合Copula函数,并估计混合Copula模型参数。首先用两阶段极大似然法估计单个Copula函数的参数。再基于经验Copula函数的最小距离法,估计混合Copula函数参数,得到对违约分布尾部刻画更精确的Copula函数模型。 (2)构建基于混合Copula函数的篮式信用违约互换定价模型,并给出基于蒙特卡洛模拟法模拟多个资产违约时间的联合分布的模拟步骤。基于Copula函数的随机数模拟方法,在已知Copula函数参数的情形下,模拟N个未来违约时间的可能情况,进而得到篮式信用违约互换第k次违约时间的数值解。本文的主要特色和创新： (1)构建混合Copula度量资产间非线性相依结构。本文构建一个基于三类阿基米德Copula的线性组合函数,即混合Copula函数。本文基于三种常用阿基米德Copula构建一种计算相对简单,分布形态灵活的混合Copula函数,并用混合Copula函数度量多个资产的违约相关性,不仅避免线性相关系数不能度量非线性相关的缺陷,而且避免了采用椭圆Copula函数对尾部相关刻画不足的问题。 (2)将混合Copula参数估计分为三个步骤,运用最小距离法选择与经验Copula拟合度最好的混合Copula,降低直接估计多个参数的难度。
[Abstract]:Credit default swaps (CDS) are off-balance sheet instruments for credit risk management in financial institutions, and they are the products with the largest trading volume of credit derivatives. Credit default swap pricing model has also become the focus of scholars at home and abroad. China version of credit default swaps-credit risk mitigation tool (CRM) has been slow to develop since its launch in 2010. The imperfection of pricing model has become one of the bottlenecks in the sustainable development of CRM market. Basket credit default swaps can effectively reduce the risk management cost and transaction cost and improve the risk management level of asset portfolio by using multiple assets as a portfolio to carry out risk management operations. It has become one of the fastest growing credit derivatives in the recent derivatives market. In this paper, the mixed Copula function is used to fit the joint distribution of default time, and the hybrid Copula function is introduced into the basket credit default swap pricing formula to establish the basket credit default swap pricing model based on mixed Copula. To provide the method and the tool for the basket type credit default swap pricing. The main work of this paper is as follows: (1) the mixed Copula function is constructed and the parameters of the mixed Copula model are estimated. First, the parameters of a single Copula function are estimated by the two-stage maximum likelihood method. Then, based on the least distance method of empirical Copula function, the parameters of mixed Copula function are estimated, and a more accurate Copula function model is obtained. (2) A basket credit default swap pricing model based on mixed Copula function is constructed. The simulation steps of simulating the joint distribution of multiple asset default times based on Monte Carlo simulation method are also given. Based on the random number simulation method of Copula function, the possible cases of N future default times are simulated under the condition of known Copula function parameters, and the numerical solution of the k-th default time of basket credit default swaps is obtained. The main features and innovations of this paper are as follows: (1) constructing a mixed Copula structure to measure the nonlinear dependence between assets. In this paper, we construct a linear combination function based on three kinds of Archimedes Copula, that is, mixed Copula function. Based on three kinds of commonly used Archimedes Copula, this paper constructs a hybrid Copula function with relatively simple calculation and flexible distribution, and uses the mixed Copula function to measure the default correlation of multiple assets. Not only to avoid the defect that linear correlation coefficient can not measure nonlinear correlation, but also to avoid the problem of using elliptical Copula function to depict tail correlation. (2) the mixed Copula parameter estimation is divided into three steps. The minimum distance method is used to select the mixed Copula with the best fitting degree of empirical Copula, which reduces the difficulty of directly estimating multiple parameters.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F832.51

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