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  本文選題：債務(wù)抵押證券　切入點：因子Copula模型　出處：《中南財經(jīng)政法大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：債務(wù)抵押證券(Collateralized Debt Obligation,簡稱CDO)是一種特殊的資產(chǎn)支持證券,是將銀行貸款、公司債券或其他信貸資產(chǎn)的現(xiàn)金流重新打包和分配而產(chǎn)生的結(jié)構(gòu)化衍生產(chǎn)品。CDO是20世紀末最具創(chuàng)新的產(chǎn)品之一,由于其靈活性受到投資者和金融機構(gòu)的青睞。然而,信用衍生產(chǎn)品的缺陷引發(fā)了2007年次貸危機,投資者開始意識到業(yè)界通用的CDO定價框架具有很大的不足。對于CDO的定價,常用的定價方法有BET模型、因子Copula模型、仿射強度模型等,而這些模型和方法不能解決“相關(guān)性微笑”等問題。因此,本文結(jié)合國內(nèi)外學(xué)者的研究成果,提出Levy因子Copula模型,對標準模型做出改進。本文分為五個部分,第一部分為導(dǎo)論,闡述了本文研究背景及意義,并總結(jié)了前人的研究成果;第二部分為CDO定價原理,根據(jù)CDO的交易結(jié)構(gòu),介紹了CDO定價的大樣本同質(zhì)性假設(shè)和無套利原理;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分布構(gòu)建因子Copula模型,并提出使用遠期違約概率構(gòu)建動態(tài)模型,給出了數(shù)值算法;第四部分本文以iTraxx Europe指數(shù)分券為例進行了數(shù)值分析和實證分析;最后一部分總結(jié)了本文的研究結(jié)論。本文的研究結(jié)果為:通過引入混合VG分布和混合NIG分布兩種Levy分布,利用其分布的厚尾性和卷積不變性,構(gòu)建了厚尾相關(guān)結(jié)構(gòu)的因子Copula模型,并推導(dǎo)出同質(zhì)性假設(shè)下Levy因子Copula模型下CDO各分券的定價公式和數(shù)值算法。針對靜態(tài)CDO定價模型的缺陷,提出使用遠期違約概率,構(gòu)造了動態(tài)模型下,標的資產(chǎn)池違約概率分布的遞推公式,給出了相應(yīng)的數(shù)值算法。通過對iTraxx指數(shù)分券的數(shù)值分析,本文發(fā)現(xiàn)Levy分布對違約概率和違約相關(guān)性的建模更有優(yōu)勢。同時,對iTraxx指數(shù)分券的市場數(shù)據(jù)的擬合結(jié)果表明,本文提出的模型具有更好的定價精度和更高的穩(wěn)定性,“相關(guān)系數(shù)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.
【學(xué)位授予單位】：中南財經(jīng)政法大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F831.51

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本文編號：1633164