分数布朗运动环境下后定选择权定价模型研究

发布时间：2018-01-22 13:32

本文关键词： 分数布朗运动 Orenstein-Uhlenback过程后定选择权分数跳-扩散过程保险精算方法　出处：《西安工程大学》2012年硕士论文　论文类型：学位论文

【摘要】：期权定价理论是金融数学研究的核心问题之一。1973年Black和Scholes假设股票价格在几何布朗运动环境下，提出了著名的Black-Scholes期权定价模型，并给出了其定价公式。然而，在实际的金融市场模型中用分数布朗运动取代标准布朗运动早已被众多学者认同，主要是由于分数布朗运动具有较好地“厚尾”和长程依赖性。本文假设股票价格满足分数布朗运动驱动的随机微分方程，建立分数布朗运动环境下的金融市场，利用分数布朗运动的随机理论和保险精算方法，研究后定选择权定价问题。全文共分六章。第一章，介绍期权定价理论的历史及研究现状、选题依据以及研究的主要内容。第二章，介绍分数布朗运动的定义及其性质，，同时介绍分数布朗运动随机分析理论及欧式期权的保险精算方法。第三章，假设股票价格满足分数布朗运动驱动的随机微分方程，利率满足Hull-White模型，利用分数布朗运动的随机分析理论及保险精算方法研究了后定选择权的定价问题，并得到了后定选择权定价公式。第四章，建立分数跳-扩散Orenstein-Uhlenback过程下的金融市场模型，利用分数跳-扩散过程理论及保险精算方法，讨论了后定选择权定价问题，获得了后定选择权定价公式。第五章，建立混合分数跳-扩散环境下的金融市场模型，利用保险精算方法和分数跳-扩散过程理论，得到了欧式期权和后定选择权的定价公式。第六章，总结本文所研究的主要结果，并提出还需进一步研究的问题。
[Abstract]:Option pricing theory is one of the core problems in financial mathematics. In 1973, Black and Scholes assumed that the stock price is in the geometric Brownian motion environment. In this paper, a famous Black-Scholes option pricing model is proposed and its pricing formula is given. Replacing standard Brownian motion with fractional Brownian motion in actual financial market model has been recognized by many scholars, mainly because fractional Brownian motion has a good "thick tail" and long range dependence. This paper assumes that the stock price satisfies the stochastic differential equation driven by the fractional Brownian motion and establishes the financial market under the fractional Brownian motion environment. The stochastic theory of the fractional Brownian motion and the actuarial method are used. The thesis is divided into six chapters. The first chapter introduces the history and research status of option pricing theory. In the second chapter, the definition and properties of fractional Brownian motion are introduced, and the stochastic analysis theory of fractional Brownian motion and the actuarial method of European option are also introduced. In chapter 3, we assume that the stock price satisfies the stochastic differential equation driven by fractional Brownian motion, and the interest rate satisfies the Hull-White model. By using the stochastic analysis theory of fractional Brownian motion and the actuarial method, the pricing problem of postdeterminate option is studied, and the pricing formula of postdeterminate option is obtained. In chapter 4th, the financial market model of fractional hop-diffusion Orenstein-Uhlenback process is established, and the theory of fractional hop-diffusion process and the actuarial method of insurance are used. In this paper, we discuss the pricing problem of postdeterminate option, and obtain the pricing formula of postdeterminate option. In Chapter 5th, the financial market model under mixed fractional hopping and diffusion environment is established, and the pricing formulas of European option and postdeterminate option are obtained by using the actuarial method and the theory of fractional hop-diffusion process. Chapter 6th summarizes the main results of this paper and points out the problems that need further study.
【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】：O211.6;F830.9

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