Copula方法在信用衍生品定价中的应用

发布时间：2018-09-14 09:13

【摘要】：信用衍生产品自诞生以来便得到了飞速的发展,作为信用衍生产品的主要品种之一,债务担保债券(CDO)也曾经一度占据了市场的大量份额,然而2008年金融危机后,曾经交易非常活跃的信用衍生品也遭到了人们的严重质疑,CDO产品更是遭受重创,几乎销声匿迹,最近两年状况才有所回转。作为CDO的主要定价方法之一,Copula方法一直都是学者们重点研究的对象,尤其是在金融危机之后,传统Copula方法所带来的定价问题更是引起了人们的关注。本文就是在这样的背景下,对以下问题进行了研究：首先本文研究了α-stable分布下的CDO定价问题。从金融危机我们可以看出,正是由于传统的高斯Copula厚尾性不足,从而导致了对极端违约事件的估计不足,因此,本文利用了α-stable分布的厚尾性质以及较高的参数自由度,使用因子Copula方法来构造更加符合实际市场数据的Copula模型；同时,由于在实际市场中,违约概率和回收率是呈负相关关系的,因此本文也考虑了回收率随机情况下的CDO定价；并且通过对比分析可以看出,α-stable Copula在CDO定价方面确实有着较好的表现。其次本文研究了动态Copula下的CDO定价问题。大部分文献都是在静态Copula的模型下对CDO进行定价,难以刻画CDO随时间变化的特征,因此本文给出了违约概率与回收率动态的相关结构,并在此基础上研究了动态Copula的定价问题,同时由于条件契贝晓夫大数定律只能对违约损失作出估计,而不能给出的在此估计下产生的误差,因此本文利用鞍点近似法,重新估算违约损失分布,并且给出了在这种方法下得到的违约损失分布的误差估计。最后本文对隐含Copula方法做作了一个简单的介绍。不同于一般的Copula方法,隐含Copula并不是通过直接构造Copula模型来对CDO进行定价的,而是通过市场数据,直接得到条件违约概率,然后与之对应的存在一个Copula,只是这个Copula我们并不知道它的结构如何,因此才被称作隐含Copula。本文介绍了如何利用隐含Copula对CDO进行定价的方法,并且考虑了这种方法可能推广的情形,这也是本文后续重点研究的内容之一。
[Abstract]:Credit derivatives have been developed rapidly since they were born. As one of the main varieties of credit derivatives, (CDO) once occupied a large market share. However, after the financial crisis in 2008, Credit derivatives, which used to be highly traded, have also been severely questioned. CDO products have been hit hard, almost disappeared, and have only turned around in the last two years. As one of the main pricing methods of CDO, Copula method has always been the focus of research, especially after the financial crisis, the traditional Copula method has attracted more and more attention. In this paper, we study the following problems: firstly, we study the CDO pricing problem under 伪 -stable distribution. From the financial crisis, we can see that it is precisely because of the insufficiency of the traditional Gao Si Copula thick tail that the extreme default events are underestimated. Therefore, this paper makes use of the thick tail property of 伪 -stable distribution and the higher degree of freedom of parameters. The factor Copula method is used to construct the Copula model which is more in line with the actual market data. At the same time, because the probability of default is negatively correlated with the recovery rate in the real market, this paper also considers the CDO pricing under the random recovery rate. And through comparative analysis, it can be seen that 伪 -stable Copula has a good performance in CDO pricing. Secondly, we study the problem of CDO pricing under dynamic Copula. Most of the literatures are pricing CDO under the static Copula model, so it is difficult to describe the characteristics of CDO changing with time. Therefore, this paper gives the correlation structure of the probability of default and the dynamic recovery rate, and then studies the pricing problem of dynamic Copula. At the same time, because the law of large numbers of conditional Chebyshev can only estimate the loss of default, but the error can not be given, the saddle point approximation method is used to reestimate the distribution of the loss of breach of contract. The error estimates of the default loss distribution obtained by this method are also given. Finally, this paper presents a brief introduction to the implicit Copula method. Unlike general Copula methods, implicit Copula does not price CDO directly by constructing Copula models, but through market data, the conditional default probability is obtained directly. And then there's a Copula, corresponding to it, which is just this Copula, and we don't know what its structure is, so it's called an implicit Copula.. In this paper, we introduce how to use implicit Copula to price CDO, and consider the possible extension of this method, which is one of the important contents of this paper.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F224;F830

【相似文献】