CDO产品定价模型的比较研究

发布时间：2018-04-26 09:44

本文选题：债券担保凭证 + 信用组合风险　；参考：《华中科技大学》2014年博士论文

【摘要】：尽管Copula方法已成为CDO定价的标准方法,但在CDO定价理论中结构化模型和简约化模型仍然具有它们独特的优势。本文以信用组合的违约相关性为切入点,从理论和实证两方面研究了这三类模型,主要研究结论如下：关于CDO定价的简约化模型。本文主要从以下三个方面展开：其一,信用风险定价的简约化理论；其二,资产组合违约相关的信用风险分析,主要从信用违约强度的角度引入违约相关性,给出信用组合的违约风险建模；其三,以资产组合信用风险分析为基础,研究CDO定价的简约化理论,重点研究可比较资产组合分散度的计算。关于CDO定价简约化理论的相关应用。本文主要以信用组合的风险模型为基础,以利率期限结构模型为参照,从四个方面对简约化模型应用所产生的问题进行了理论和实证分析：(1)从理论层面指出实证研究中简约模型的参数估计值会出现不稳定性问题,研究表明传统数值方法并不能保证得到的估计值是全局最大值；(2)理论上比较了CDO简约模型与利率期限结构模型,研究表明它们是同一建模方法的两个应用;(3)以利率期限结构模型为基础给出简约化模型完整的实证过程,这为CDO的实证研究提供了参考,研究表明参数估计值的稳定性高度依赖数值方法初始值的选择,估计结果是否是似然函数的全局最大值值得商榷；(4)基于最小卡方(Minimum-Chi-Square, MCS)方法研究了高斯模型的识别性问题并给出了实证结论。理论研究表明MCS方法的参数估计值继承了极大似然法的所有渐进性质,并且能够保证估计值是全局最大值,在计算效率上MCS方法远优于后者。关于CDO定价的Copula方法。从Copula函数的基本理论出发,给出了CDO定价因子Copula方法的相关理论,主要包括以下几个方面：(1)从Copula函数的相关理论出发,研究了两类典型的Copula函数即标准型和阿基米德Copula,并且分别给出了它们的随机数模拟过程；(2)研究了n维Copula函数的抽样理论,为Copula方法的模拟提供了基础；(3)CDO定价的因子Copula相关理论,主要介绍了高斯Copula模型和t-Copula模型。关于CDO定价的结构化方法。结构化模型的理论基础为首达模型,以此为基础得到了信用组合违约风险建模和CDO定价结构化模型,具体内容如下：(1)信用组合的结构化模型研究表明随着修正违约距离MDD的增大,信用利差逐渐缩小。(2)信用组合的CDO结构化定价理论主要包括违约阈值的模拟思想以及CDO结构化模型定价,资产组合信用违约阈值的选择必须与首达时间概率分布以及违约概率密度函数相一致。(3)理论上给出CDO结构模型与Copula建模方法的比较,研究表明高斯Copula刻画的违约相关性是结构化模型给出的违约相关性的有效近似,两种方法给出的CDO定价差异性不大。
[Abstract]:Although the Copula method has become the standard method of CDO pricing, the structured model and simplified model in the CDO pricing theory still have their unique advantages. This paper studies the three types of models from two aspects of theory and demonstration. The main conclusions are as follows:
On the simplified model of CDO pricing, this paper mainly starts from the following three aspects: first, the simplified theory of credit risk pricing; secondly, the analysis of credit risk related to the default of asset portfolio, mainly from the perspective of the strength of the credit default, to give the default risk modeling of the credit combination; thirdly, the combination of the asset portfolio. On the basis of credit risk analysis, we study the simplification theory of CDO pricing, and focus on the calculation of the dispersion of comparable assets.
Based on the risk model of the credit combination and taking the term structure model of the interest rate as the reference, this paper makes a theoretical and empirical analysis of the problems arising from the application of the simplified model from four aspects: (1) the parameter estimation of the simplified model in the empirical study is pointed out from the theoretical level. The problem of instability shows that the traditional numerical method does not guarantee the global maximum value. (2) the CDO simplification model and the interest rate term structure model are compared theoretically. The study shows that they are the two applications of the same modeling method; (3) the simplified model is complete on the basis of the term structure model of interest rate. The empirical study provides a reference for the empirical study of CDO. The study shows that the stability of the parameter estimation is highly dependent on the selection of the initial value of the numerical method and the global maximum of the likelihood function is debatable. (4) based on the least square (Minimum-Chi-Square, MCS) method, the identification problem of the Gauss model is studied and given. The theoretical study shows that the parameter estimation of the MCS method inherits all the asymptotic properties of the maximum likelihood method and can ensure that the estimated value is the global maximum, and the MCS method is far superior to the latter in the computational efficiency.
On the basis of the basic theory of Copula function, based on the basic theory of the Copula function, the relevant theories of the CDO pricing factor Copula method are given. The following are the following aspects: (1) starting from the related theory of Copula function, two typical Copula functions, the standard type and Archimedes Copula, are studied, and their random properties are given respectively. The numerical simulation process; (2) the sampling theory of the n-dimensional Copula function is studied, which provides the basis for the simulation of Copula method; (3) the factor Copula related theory of CDO pricing, mainly introducing the Gauss Copula model and the t-Copula model.
On the structured method of CDO pricing, the theoretical basis of structured model is the first model. On this basis, the credit combination default risk modeling and the CDO pricing structure model are obtained. The specific contents are as follows: (1) the structural model of the credit combination shows that the credit spreads gradually diminishes with the increase of the revised default distance MDD. (2) credit The combined CDO structured pricing theory mainly includes the simulation thought of default threshold and the pricing of CDO structured model. The selection of the portfolio credit default threshold must be consistent with the probability distribution of the first time and the probability density function of default. (3) the comparison of the CDO structure model with the Copula modeling method is given in theory, and the research shows that Gauss Co The default correlation described by Pula is an effective approximation of the default correlation given by the structured model. The difference between the two methods of CDO pricing is not large.

【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F224;F830.91

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