本文選題：違約債券　切入點(diǎn)：隨機(jī)利率　出處：《廣西師范大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：信用風(fēng)險(xiǎn)是當(dāng)今金融數(shù)學(xué)領(lǐng)域一個(gè)十分重要的研究課題,信用風(fēng)險(xiǎn)管理的核心內(nèi)容之一是違約債券的定價(jià).公司債券作為一種違約風(fēng)險(xiǎn)證券,是指企業(yè)為了籌集外部資金而發(fā)行的一種債務(wù)憑證.當(dāng)公司總資產(chǎn)價(jià)值不足以支付債務(wù)時(shí),違約就會發(fā)生.現(xiàn)代金融理論對于公司債券的研究,主要分為結(jié)構(gòu)化方法和簡約化方法兩大類.然而在現(xiàn)實(shí)的金融市場中,一個(gè)貼近實(shí)際以及有效的市場模型在投資決策、風(fēng)險(xiǎn)規(guī)避和管理等方面有著重要的作用.盡管經(jīng)典Black-Scholes模型有著許多優(yōu)勢及符合實(shí)際的意義,但是過于理想化的假設(shè),導(dǎo)致其計(jì)算結(jié)果與實(shí)際市場的觀測數(shù)據(jù)存在較大偏差.為了能夠合理刻畫市場變量的實(shí)際變動(dòng)規(guī)律,很多學(xué)者都對Black-Scholes模型進(jìn)行改進(jìn),嘗試建立能更好擬合金融市場的數(shù)學(xué)模型.1974年Merton首先建立了公司總資產(chǎn)價(jià)值的結(jié)構(gòu)化模型并對公司債券進(jìn)行了研究,之后在Merton的基礎(chǔ)上許多學(xué)者都進(jìn)行了更加深入的研究,取得了豐富的成果.這些研究主要集中在公司資產(chǎn)的行為建模方面,它們是引入跳擴(kuò)散過程、隨機(jī)波動(dòng)率和隨機(jī)利率等貼近實(shí)際的數(shù)學(xué)模型.本文采用結(jié)構(gòu)化方法,在標(biāo)的資產(chǎn)引入跳擴(kuò)散過程的基礎(chǔ)上綜合考慮波動(dòng)率和利率帶跳的情形,并討論公司違約債券的定價(jià),該模型具有一般性,更加符合實(shí)際.主要工作包括： 第一章介紹了本文的研究意義,國內(nèi)外研究現(xiàn)狀,以及本文的選題依據(jù). 第二章在利率帶跳的情形下研究了公司違約債券的定價(jià),主要應(yīng)用Fourier反變換、偏微分方程和Feynman-Kac定理等隨機(jī)分析方法得到了公司違約債券價(jià)格的顯式解,并應(yīng)用計(jì)算實(shí)例分析模型各參數(shù)對可違約債券價(jià)格的影響. 第三章在第二章模型的基礎(chǔ)上綜合考慮隨機(jī)波動(dòng)率帶跳情形下的公司違約債券定價(jià).主要應(yīng)用偏微分方程,黎卡提方程和Feynman-Kac定理等隨機(jī)分析方法得到了公司違約債券的顯式解,并通過一些計(jì)算實(shí)例分析波動(dòng)率變量的敏感性. 第四章總結(jié)本文的主要工作和有待進(jìn)一步研究的問題.
[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.
【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F830.91;F224

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本文編號：1631565