基于Hull-White模型的附息票债券期权定价研究

发布时间：2018-02-28 07:38

本文关键词： 分数布朗运动逼近的分数布朗运动过程混合分数布朗运动 Hull-White模型附息票债券期权　出处：《西安工程大学》2012年硕士论文　论文类型：学位论文

【摘要】：期权定价一直是金融学和计量经济学上研究热点.近年来,除了对熟知的欧式期权和美式期权进行研究外,国内外也有很多研究是基于不同标的资产的期权定价.课题主要研究了标的资产为附息票债券的期权分别在分数布朗运动、鞅过程逼近的分数布朗运动、混合分数布朗运动所驱动的市场下定价模型及其解析解. 第一章和第二章分别是绪论和预备知识.绪论首先介绍了期权、期权定价理论的历史,及利率期权定价研究的发展过程.然后,阐述了课题的研究背景和意义,及目前国内外的研究现状.第二章则简单介绍了本课题在研究过程中将用到的基础理论知识. 第三章研究了分数布朗运动环境下,短期利率满足Hull-White模型.利用市场无套利原理、分数Ito公式等,得到零息票债券价格公式,利用分数布朗运动下的随机理论、偏微分方程方法等,得到了期权定价模型解析解. 第四章主要针对分数布朗运动不具有鞅性的问题,定义随机积分其中是一个半鞅.最终,我们得到附息票债券期权定价公式. 第五章用混合分数布朗运动驱动金融市场,噪声与半鞅有着相类似的性质.当驱动的市场完备且无套利.本章在Hull-White模型下,利用一个半鞅逼近分数布朗运动的价格过程,并给出了附息票债券期权定价模型及其解析解. 第六章对本文研究的主要结果做出总结,并提出了未来的研究目标和方向.
[Abstract]:Option pricing has been a hot topic in finance and econometrics. In recent years, in addition to the well-known European options and American options, At home and abroad, there are many researches based on the option pricing of different underlying assets. In this paper, we mainly study the fractional Brownian motion in fractional Brownian motion and the fractional Brownian motion in martingale process in which the underlying asset is an interest-bearing bond. The pricing model driven by mixed fractional Brownian motion and its analytical solution. The first chapter introduces the history of options, option pricing theory, and the development process of interest rate option pricing. The second chapter briefly introduces the basic theory knowledge which will be used in the research process. In chapter 3, we study the Hull-White model of short-term interest rate under fractional Brownian motion. Using the market no-arbitrage principle and fractional Ito formula, we obtain the zero-coupon bond price formula, and use the stochastic theory of fractional Brownian motion. The analytical solution of option pricing model is obtained by partial differential equation method and so on. In Chapter 4th, for the problem that fractional Brownian motion is not martingale, we define stochastic integral which is a semimartingale. Finally, we obtain the pricing formula of coupon bond option. In Chapter 5th, the mixed fractional Brownian motion is used to drive the financial market, and the noise is similar to that of the semimartingale. When the driven market is complete and has no arbitrage, this chapter uses a semi-martingale to approximate the price process of the fractional Brownian motion under the Hull-White model. An option pricing model and its analytical solution are given. Chapter 6th summarizes the main results of this paper, and proposes the future research objectives and directions.
【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

【参考文献】