结构化跳扩散模型下公司违约债券定价

发布时间：2018-03-18 22:24

本文选题：违约债券　切入点：随机利率　出处：《广西师范大学》2012年硕士论文　论文类型：学位论文

【摘要】：信用风险是当今金融数学领域一个十分重要的研究课题,信用风险管理的核心内容之一是违约债券的定价.公司债券作为一种违约风险证券,是指企业为了筹集外部资金而发行的一种债务凭证.当公司总资产价值不足以支付债务时,违约就会发生.现代金融理论对于公司债券的研究,主要分为结构化方法和简约化方法两大类.然而在现实的金融市场中,一个贴近实际以及有效的市场模型在投资决策、风险规避和管理等方面有着重要的作用.尽管经典Black-Scholes模型有着许多优势及符合实际的意义,但是过于理想化的假设,导致其计算结果与实际市场的观测数据存在较大偏差.为了能够合理刻画市场变量的实际变动规律,很多学者都对Black-Scholes模型进行改进,尝试建立能更好拟合金融市场的数学模型.1974年Merton首先建立了公司总资产价值的结构化模型并对公司债券进行了研究,之后在Merton的基础上许多学者都进行了更加深入的研究,取得了丰富的成果.这些研究主要集中在公司资产的行为建模方面,它们是引入跳扩散过程、随机波动率和随机利率等贴近实际的数学模型.本文采用结构化方法,在标的资产引入跳扩散过程的基础上综合考虑波动率和利率带跳的情形,并讨论公司违约债券的定价,该模型具有一般性,更加符合实际.主要工作包括：第一章介绍了本文的研究意义,国内外研究现状,以及本文的选题依据. 第二章在利率带跳的情形下研究了公司违约债券的定价,主要应用Fourier反变换、偏微分方程和Feynman-Kac定理等随机分析方法得到了公司违约债券价格的显式解,并应用计算实例分析模型各参数对可违约债券价格的影响. 第三章在第二章模型的基础上综合考虑随机波动率带跳情形下的公司违约债券定价.主要应用偏微分方程,黎卡提方程和Feynman-Kac定理等随机分析方法得到了公司违约债券的显式解,并通过一些计算实例分析波动率变量的敏感性. 第四章总结本文的主要工作和有待进一步研究的问题.
[Abstract]:Credit risk is a very important research subject in the field of financial mathematics. One of the core contents of credit risk management is the pricing of defaulting bonds. A debt certificate issued by an enterprise in order to raise external funds. Default occurs when the total asset value of a company is insufficient to pay the debt. It is mainly divided into two categories: structured method and minimization method. However, in the real financial market, a realistic and effective market model is used to make investment decisions. Risk aversion and management play an important role. Although the classical Black-Scholes model has many advantages and practical significance, it is too idealized. In order to describe the actual variation of market variables reasonably, many scholars have improved the Black-Scholes model. In 1974, Merton first established the structured model of the total asset value of the company and studied the corporate bonds, and then many scholars carried out more in-depth research on the basis of Merton. These researches are mainly focused on the behavioral modeling of corporate assets. They are mathematical models which are close to reality, such as jump diffusion process, random volatility and random interest rate, etc. In this paper, a structured method is used. On the basis of introducing jump diffusion process into underlying assets, the volatility and interest rate with jump are considered synthetically, and the pricing of corporate default bonds is discussed. The model is general and more practical. The main work includes:. The first chapter introduces the significance of this study, domestic and foreign research status, as well as the basis of this topic. In the second chapter, we study the pricing of corporate default bonds under the condition of interest rate jump. We use Fourier inverse transformation, partial differential equation and Feynman-Kac theorem to obtain the explicit solution of corporate default bond price. The influence of each parameter of the model on the price of defaultable bonds is analyzed by using a computational example. In chapter 3, we consider the pricing of corporate default bonds with random volatility on the basis of the model in chapter 2. Some stochastic analysis methods such as Riccati equation and Feynman-Kac theorem are used to obtain the explicit solution of corporate default bonds. Some examples are given to analyze the sensitivity of volatility variables. Chapter 4th summarizes the main work of this paper and the problems to be further studied.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;F224

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