基于Levy因子Copula模型的CDO定价分析

发布时间：2018-03-19 06:16

本文选题：债务抵押证券　切入点：因子Copula模型　出处：《中南财经政法大学》2017年硕士论文　论文类型：学位论文

【摘要】：债务抵押证券(Collateralized Debt Obligation,简称CDO)是一种特殊的资产支持证券,是将银行贷款、公司债券或其他信贷资产的现金流重新打包和分配而产生的结构化衍生产品。CDO是20世纪末最具创新的产品之一,由于其灵活性受到投资者和金融机构的青睐。然而,信用衍生产品的缺陷引发了2007年次贷危机,投资者开始意识到业界通用的CDO定价框架具有很大的不足。对于CDO的定价,常用的定价方法有BET模型、因子Copula模型、仿射强度模型等,而这些模型和方法不能解决“相关性微笑”等问题。因此,本文结合国内外学者的研究成果,提出Levy因子Copula模型,对标准模型做出改进。本文分为五个部分,第一部分为导论,阐述了本文研究背景及意义,并总结了前人的研究成果;第二部分为CDO定价原理,根据CDO的交易结构,介绍了CDO定价的大样本同质性假设和无套利原理;在第三部分本文提出了Levy因子Copula模型,引入混合VG分布和混合NIG分布构建因子Copula模型,并提出使用远期违约概率构建动态模型,给出了数值算法;第四部分本文以iTraxx Europe指数分券为例进行了数值分析和实证分析;最后一部分总结了本文的研究结论。本文的研究结果为:通过引入混合VG分布和混合NIG分布两种Levy分布,利用其分布的厚尾性和卷积不变性,构建了厚尾相关结构的因子Copula模型,并推导出同质性假设下Levy因子Copula模型下CDO各分券的定价公式和数值算法。针对静态CDO定价模型的缺陷,提出使用远期违约概率,构造了动态模型下,标的资产池违约概率分布的递推公式,给出了相应的数值算法。通过对iTraxx指数分券的数值分析,本文发现Levy分布对违约概率和违约相关性的建模更有优势。同时,对iTraxx指数分券的市场数据的拟合结果表明,本文提出的模型具有更好的定价精度和更高的稳定性,“相关系数微笑”的程度也越小。
[Abstract]:Collateralized Debt obligation (CDO) is a special kind of asset-backed securities, is a bank loan, Structured derivatives generated by the repackaging and allocation of cash flow from corporate bonds or other credit assets. CDO was one of the most innovative products at the end of 20th century, and was favored by investors and financial institutions because of its flexibility. The defects of credit derivatives caused the subprime mortgage crisis in 2007, and investors began to realize that the general CDO pricing framework has great shortcomings. For the pricing of CDO, the commonly used pricing methods are BET model, factor Copula model. Affine intensity model and so on, but these models and methods can not solve the problem such as "correlation smile". Therefore, this article combines the domestic and foreign scholars' research results, proposes the Levy factor Copula model, makes the improvement to the standard model. The first part introduces the background and significance of this paper, and summarizes the previous research results. The second part is the CDO pricing principle, according to the structure of CDO, the large sample homogeneity hypothesis and arbitrage principle of CDO pricing are introduced. In the third part, the Levy factor Copula model is proposed, the mixed VG distribution and mixed NIG distribution are introduced to construct the factor Copula model, and the dynamic model is constructed by using the long term default probability, and the numerical algorithm is given. In the 4th part, we take the iTraxx Europe index coupon as an example to carry on the numerical analysis and the empirical analysis; the last part summarizes the research conclusion of this paper. The results of this paper are as follows: by introducing the mixed VG distribution and the mixed NIG distribution two kinds of Levy distribution, Based on the distribution of thick tail and convolution invariance, the factor Copula model of thick tail correlation structure is constructed, and the pricing formula and numerical algorithm of CDO coupon under Levy factor Copula model under homogeneity assumption are derived. In this paper, the recursive formula of default probability distribution of underlying asset pool under dynamic model is constructed by using forward default probability, and the corresponding numerical algorithm is given. In this paper, we find that Levy distribution has more advantages in modeling the probability of default and the correlation of default. At the same time, the fitting results of the market data of iTraxx index securities show that, The proposed model has better pricing accuracy and higher stability, and the degree of "correlation coefficient smile" is smaller.
【学位授予单位】：中南财经政法大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F831.51

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