分数布朗运动环境下可换债券定价模型

发布时间：2018-03-11 06:28

本文选题：分数布朗运动　切入点：可转换债券　出处：《西安工程大学》2012年硕士论文　论文类型：学位论文

【摘要】：可转换公司债券又称可转换债券，其本质仍属于债券故仍以债券的形式发行，所不同的是在发行之初，其所属发行公司规定债券持有人可以自行选择在债券到期当日或之前的某一天按约定的转换比率将其持有的债券转换成发行公司的股票。它兼具债券和期权的特征，能够为发行者和持有人创造双赢利益，逐步成为一种新兴金融衍生产品。分数布朗运动因其具有相关性、长程关联性和自相似性，与人们对金融市场的现实感觉更为贴合，，逐步发展成一种主流的新型金融研究工具。本文在分数布朗运动环境的金融市场模型下，对可转换债券的价值构成和定价公式进行了研究。全文共分为八章。第一章，主要介绍了可转换债券的研究现状、发展动态、选题依据、研究意义，以及主要的研究内容。第二章，介绍了分数布朗运动的概念、性质，分数布朗运动的随机积分相关定理，并对可转换债券模型给出定义。第三章，假定利率、波动率、红利率均为常数情况下建立股票价格过程服从几何分数布朗运动的金融市场数学模型，得到了分数布朗运动环境下带交易成本的可转换债券的定价公式。第四章，假定无风险利率、期望收益率、股票波动率和红利率均为时间的确性函数条件下，建立分数布朗运动环境下的金融市场数学模型，利用分数布朗随机分析理论，得到了具有支付红利的可转换债券定价公式。第五章，假定随机利率满足Vasicek模型下，建立股票价格服从几何分数布朗运动的金融市场数学模型，利用保险精算方法，得到了随机利率下具有支付红利的可转换债券的定价公式。第六章，假定股票价格服从带跳的分数布朗运动，利率满足Vasicek模型，建立分数跳-扩散环境下金融市场数学模型，利用保险精算方法和分数布朗运动随机分析理论，得到了随机利率下具有支付红利的可转换债券的定价公式。第七章，假定股票价格和企业资产价值均服从分数布朗运动驱动的随机微分方程，利率为时间的确定性函数，建立了分数布朗运动环境下金融市场数学模型，利用保险精算方法，得到了具有违约风险的可转换债券定价公式。第八章，总结了本文主要研究成果，并提出进一步研究问题。
[Abstract]:Convertible corporate bonds, also known as convertible bonds, are still bonds in nature, so they are still issued in the form of bonds. Its issuing company provides that bondholders may, at their own option, convert their holdings of bonds into shares of the issuing company at an agreed conversion rate on or before the date of maturity of the bonds. It has the characteristics of both bonds and options, It can create win-win benefits for issuers and holders, and gradually become an emerging financial derivative. Because of its relevance, long-term relevance and self-similarity, the fractional Brownian movement is more relevant to the reality of financial markets. Gradually developed into a mainstream new financial research tools. In this paper, the value composition and pricing formula of convertible bonds are studied under the financial market model of fractional Brownian motion environment. The whole paper is divided into eight chapters. The first chapter mainly introduces the research status, the development trend, the topic selection basis, the research significance and the main research content of convertible bonds. In the second chapter, we introduce the concept and properties of fractional Brownian motion, the stochastic integral correlation theorem of fractional Brownian motion, and give the definition of convertible bond model. In chapter 3, assuming that interest rate, volatility and red interest rate are all constant, a financial market mathematical model of stock price process using geometric fractional Brownian motion is established. The pricing formula of convertible bonds with transaction cost in fractional Brownian motion is obtained. In Chapter 4th, assuming that the risk-free interest rate, the expected rate of return, the stock volatility and the dividend rate are all time certainty functions, the financial market mathematical model under the fractional Brownian motion environment is established, and the fractional Brownian stochastic analysis theory is used. The pricing formula of convertible bonds with dividend payment is obtained. In Chapter 5th, assuming that the stochastic interest rate satisfies the Vasicek model, a financial market mathematical model of stock price with geometric fractional Brownian motion is established, and the actuarial method is used. The pricing formula of convertible bonds with dividend payment at random interest rate is obtained. In Chapter 6th, assuming that the stock price moves from fractional Brownian motion with jump, the interest rate satisfies the Vasicek model, the mathematical model of financial market in the environment of fractional hopping and diffusion is established, and the stochastic analysis theory of fractional Brownian motion is used by means of actuarial method and fractional Brownian motion. The pricing formula of convertible bonds with dividend payment at random interest rate is obtained. In Chapter 7th, assuming that both the stock price and the value of the firm's assets are governed by stochastic differential equations driven by fractional Brownian motion, and the interest rate is a deterministic function of time, a mathematical model of financial market in the environment of fractional Brownian motion is established. By means of actuarial method, a convertible bond pricing formula with default risk is obtained. Chapter 8th, summarized the main research results of this paper, and put forward further research problems.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;O211.6

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