Copula方法在信用衍生品定價(jià)中的應(yīng)用
發(fā)布時(shí)間：2018-09-14 09:13
【摘要】：信用衍生產(chǎn)品自誕生以來便得到了飛速的發(fā)展,作為信用衍生產(chǎn)品的主要品種之一,債務(wù)擔(dān)保債券(CDO)也曾經(jīng)一度占據(jù)了市場的大量份額,然而2008年金融危機(jī)后,曾經(jīng)交易非�；钴S的信用衍生品也遭到了人們的嚴(yán)重質(zhì)疑,CDO產(chǎn)品更是遭受重創(chuàng),幾乎銷聲匿跡,最近兩年?duì)顩r才有所回轉(zhuǎn)。作為CDO的主要定價(jià)方法之一,Copula方法一直都是學(xué)者們重點(diǎn)研究的對象,尤其是在金融危機(jī)之后,傳統(tǒng)Copula方法所帶來的定價(jià)問題更是引起了人們的關(guān)注。本文就是在這樣的背景下,對以下問題進(jìn)行了研究： 首先本文研究了α-stable分布下的CDO定價(jià)問題。從金融危機(jī)我們可以看出,正是由于傳統(tǒng)的高斯Copula厚尾性不足,從而導(dǎo)致了對極端違約事件的估計(jì)不足,因此,本文利用了α-stable分布的厚尾性質(zhì)以及較高的參數(shù)自由度,使用因子Copula方法來構(gòu)造更加符合實(shí)際市場數(shù)據(jù)的Copula模型；同時(shí),由于在實(shí)際市場中,違約概率和回收率是呈負(fù)相關(guān)關(guān)系的,因此本文也考慮了回收率隨機(jī)情況下的CDO定價(jià)；并且通過對比分析可以看出,α-stable Copula在CDO定價(jià)方面確實(shí)有著較好的表現(xiàn)。 其次本文研究了動(dòng)態(tài)Copula下的CDO定價(jià)問題。大部分文獻(xiàn)都是在靜態(tài)Copula的模型下對CDO進(jìn)行定價(jià),難以刻畫CDO隨時(shí)間變化的特征,因此本文給出了違約概率與回收率動(dòng)態(tài)的相關(guān)結(jié)構(gòu),并在此基礎(chǔ)上研究了動(dòng)態(tài)Copula的定價(jià)問題,同時(shí)由于條件契貝曉夫大數(shù)定律只能對違約損失作出估計(jì),而不能給出的在此估計(jì)下產(chǎn)生的誤差,因此本文利用鞍點(diǎn)近似法,重新估算違約損失分布,并且給出了在這種方法下得到的違約損失分布的誤差估計(jì)。 最后本文對隱含Copula方法做作了一個(gè)簡單的介紹。不同于一般的Copula方法,隱含Copula并不是通過直接構(gòu)造Copula模型來對CDO進(jìn)行定價(jià)的,而是通過市場數(shù)據(jù),直接得到條件違約概率,然后與之對應(yīng)的存在一個(gè)Copula,只是這個(gè)Copula我們并不知道它的結(jié)構(gòu)如何,因此才被稱作隱含Copula。本文介紹了如何利用隱含Copula對CDO進(jìn)行定價(jià)的方法,并且考慮了這種方法可能推廣的情形,這也是本文后續(xù)重點(diǎn)研究的內(nèi)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 偽 -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 偽 -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 偽 -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.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2012
【分類號】：F224;F830
[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 偽 -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 偽 -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 偽 -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.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2012
【分類號】：F224;F830
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