【作者】 陈田；

【导师】 秦学志；

【作者基本信息】 大连理工大学 ， 金融工程， 2010， 博士

【摘要】 债务抵押债券(CDO)是一种新兴的组合类信用衍生产品,基于抵押债务的信用,通过资产证券化技术,将债券、贷款等金融资产组建资产池,重新分割投资回报和风险,以满足不同投资者的需要。自1987年由Drexel Burnham Lamert创立以来,该产品因其独特的收益风险特征得到迅速发展,成为最具典型的结构化金融创新工具。据美国证券行业和金融市场协会(SIFMA)统计,CDO近十年的全球发行量累计已超过两万亿美元。特别地,自2007年源于美国住房抵押贷款的金融危机以来,CDO的定价模型和风险管理得到了理论界和实务界的广泛关注。作为一种组合类信用衍生产品,CDO定价的关键是如何由标的资产的违约率、回收率、提前偿付率及各个资产之间的相关性得到资产池的损失分布。因此,本文直面金融危机以来的宏观经济背景和信用风险态势,紧扣CDO市场发展和研究热点,借鉴国内外现有的相关研究成果,着眼于CDO资产池损失的“尖峰厚尾”特征和“动态相关”特性,兼顾CDO标的资产的随机回收率和提前偿付率,构建了基于因子Copula的定价模型并进行了数值模拟,相关研究成果简述如下：(1)针对标准高斯因子Copula模型的“相关性微笑”现象,将资产价值的市场共同因子和个体异质因子分别用混合高斯分布和标准高斯分布刻画,建立了随机相关结构条件下基于混合高斯因子Copula的CDO定价模型,有效减弱了“相关性微笑”现象对CDO定价准确性的影响。在贝努利随机相关结构和三状态随机相关结构条件下,给出了CDO资产池损失分布的具体表达式,进而基于CDO分券层损失面的预期损失与收益面的预期收益相等的无套利定价原理,得出了CDO分券层在贝努利随机相关结构下的合理信用价差。(2)针对CDO资产池损失分布的“尖峰厚尾”特征,将资产价值的市场共同因子和个体异质因子用标准高斯和NIG的混合分布刻画,利用半解析法和傅里叶变换及其逆变换等建立了随机相关结构和局部相关结构条件下的混合NIG因子Copula定价模型,弥补了CDO资产池损失的“尖峰厚尾”特征和“动态相关”特性等风险因素刻画方面的不足。采用随机相关和局部相关两种形式刻画相关结构。随机相关结构中重点讨论贝努利相关和三状态相关两种情形；局部相关结构中主要分析相关系数服从两点分布的形式。利用傅里叶变换及其逆变换,得出了CDO资产池损失分布的求解方法。(3)针对回收率为常数的CDO定价模型“相关性微笑”、高级分券层定价失效的不足,通过将回收率设定为系统性风险这一市场共同因子的函数,构建了考虑回收率随机特征的CDO因子Copula定价模型,使之适宜于高分券层价差的估算。综合考虑了回收率的下列三种特征：随机回收率、市场共同因子服从混合高斯分布及用贝努利相关、三状态相关刻画的随机相关结构。通过对资产池违约边界、随机回收率和CDO分券层定价的数值模拟,发现：混合高斯分布可以有效地用于刻画市场共同因子这一系统性风险因素的尾部特征；随机回收率可较有效地用于刻画回收率与市场共同因子及违约相关结构的市场特征。上述特点为CDO高分券层价差的较合理估算奠定了基础。(4)针对标的资产为信贷资产等有提前偿付风险的CDO产品,通过高斯OU强度过程,结合Levy因子Copula结构,构建了考虑提前偿付风险因素的CDO因子Copula定价模型,实现了CDO定价中提前偿付因素的风险度量。利用高斯OU过程来模拟提前偿付强度和违约强度之间的动态相关性,并以Shifted Gamma过程为例,将因子Copula结构由标准高斯因子Copula推广到了Levy因子Copula,以更好地拟合金融市场的“厚尾”特征和“跳扩散”现象。在此基础上,得到了CDO资产池提前偿付分布和违约损失分布的计算方法和CDO分券层价差的半解析解。综上所述,本文从CDO的因子Copula定价模型入手,着力考察了影响CDO定价准确性的厚尾因子Copula结构、相关系数、违约回收率和提前偿付率等四个因素,藉此丰富完善了因子Copula定价模型。特别地,数值模拟表明,本文构建的因子Copula定价模型较现有模型在解决CDO定价中的“相关性微笑”、高分券层定价失效和提前偿付风险度量等方面有一定的优势,相应的研究成果有益于为金融机构CDO等结构化金融工具的产品设计与风险管理提供新思路。更多还原

【Abstract】 As a new class of credit derivatives portfolio, Collateralized Debt Obligations (CDO) securitizes bonds, loans and other financial assets into an assets pool to re-split return and risk for diversified investors, based on mortgage debt credit. Since first issuance in 1987 by Drexel Burnham Lambert, CDO has got a tremendous growth due to its unique profit/risk characteristics and has become the most typical structured instrument of financial innovations. According to statistics of Securities Industry and Financial Markets Association (SIFMA), the total global CDO issuance in recent 10 years has more than 2 trillion U.S. dollars. In particular, since the 2007 financial crisis originated by the U.S. Subprime Mortgage, CDO pricing models and risk management have been widespread community concerned in theory and practice. As a credit derivatives portfolio, the key of CDO pricing is how to get the loss distribution of assets pool by default rates, recovery rates, prepayment rates of the underlying assets and correlations between different underlying assets. Therefore, facing the macroeconomic background and credit risk situation after the financial crisis, closely concentrating on CDO market development and research focus, referring to existing relevant research outcomes, focusing on the fat tail and dynamic correlation characteristics of the CDO assets pool loss, and accounting for the random recovery rates and prepayment rates of CDO underlying assets, this paper constructed several CDO pricing models based on factor Copula and calibrated the models by numerical simulations. The relevant research results are summarized below:(1) Aiming at the "Correlation Smile" in the standard Gaussian Factor Copula model, this dissertation expresses the common market factor as the mixtures of Gaussian distributions and idiosyncratic factor as standard Gaussian distribution, and constructs CDO Pricing model based on Gaussian mixture factor Copula of the stochastic correlation structures. All of the above effectively amends CDO pricing’s error caused by the "Correlation Smile".Under the conditions of Bernoulli stochastic correlation structure and three-state stochastic correlation structure, this dissertation gives the specific expression of the cumulative default loss probability distribution for the entire assets pool, based on the no-arbitrage pricing theory where CDO tranches’expected loss is equal to its expected premium, then obtains CDO tranches’credit spread of Bernoulli stochastic correlation structure. (2) Aiming at the fat tail characteristics of the CDO assets pool loss, this dissertation expresses the common market factor and idiosyncratic factor as the mixtures of standard Gaussian distributions and NIG distribution, constructs CDO Pricing model based on NIG mixture factor Copula of the stochastic correlation structure and local correlation structure by the semi-analytical method and the Fourier transform and its inverse transform, and improves the risk measure of the fat tail and dynamic correlation characteristics of the CDO assets pool loss.We consider two correlation structures:the stochastic correlation structure and the local correlation structure, focus on Bernoulli stochastic correlation structure and three-state stochastic correlation structure for the stochastic correlation structure; analyze the two points distribution case for local correlation structure, and derive the CDO assets pool cumulative loss by Fourier transform and its inverse transform.(3) Aiming at the "Correlation Smile" and senior tranches’pricing failure in the standard Gaussian Factor Copula model where the recovery rate is a deterministic constant, this dissertation expresses the recovery rate as a function of common market factor for systemic risk, and constructs CDO factor Copula Pricing model based on random recovery to suitable for senior tranches’spread pricing.We consider the recovery with the following three features:random recovery rate, the common market factor as the mixtures of Gaussian distributions, Bernoulli and three-state stochastic correlation structure. After the numerical simulations for default barriers of assets pool, random recovery and CDO tranche pricing, it is shown that the model with Gaussian mixture factor copula can capture fat-tails, and the random recovery model can be used to describe the system risk and default correlations effectively. The features above lay the foundation for more reasonable estimate of CDO senior tranches spread.(4) Aiming at CDO products based on loans and other underlying assets with prepayment risk, using the Gaussian OU intensities process and the Levy factor Copula structure, we construct a CDO factor Copula pricing model based on prepayment risk, and realize the risk measure of prepayment risk in CDO pricing models.By capturing the negative correlation between the default and prepayment intensities via the Gaussian OU process, this dissertation introduces the Shifted Gamma process to extend the standard Gaussian factor Copula model to Levy factor Copula model in order to better fit the fat-fail and jump diffusion of financial markets. On this basis, it derives the calculating method for the prepayment distribution and default loss distribution of CDO assets pool, and then gets the semi-analytical solution of CDO tranches’spread.In summary, focusing on CDO factor Copula pricing model, this paper studied the risk factors of CDO pricing accuracy by the fat-tail factor Copula, correlation coefficient, recovery rate and prepayment rates, enriched and improved the factor Copula pricing model. In particular, numerical simulations shows that our factor Copula pricing models better fit the "Correlation Smile", senior tranches’pricing failure and risk measure of prepayment risk in CDO pricing models compared with the existing models, the corresponding research results are useful to provide new ideas about products design and risk management of CDOs and other structured financial instruments for financial institutions.更多还原