混合分数布朗运动驱动下的欧式期权定价研究

发布时间：2018-02-24 18:20

本文关键词： 混合分数布朗运动随机过程伊藤定理欧式期权欧式幂期权　出处：《广西师范学院》2013年硕士论文　论文类型：学位论文

【摘要】：本文考虑的是风险证券价格受多个分数布朗运动与一个布朗运动组合影响的两个期权定价问题:混合分数布朗运动下的欧式期权定价问题和混合分数布朗运动环境下的欧式幂期权定价问题. 首先,本文在第一章介绍了当前金融行业的研究背景,得出我国在未来金融衍生工具领域里有着巨大的潜力的结论.然后通过介绍期权定价理论的产生与发展,能让人们更加直观的了解到期权的发展历程,为目前研究期权问题的人们提供理论基础.接下来介绍了本文的研究工作.在此前,文献[1]研究过风险证券价格受一个分数布朗运动与一个布朗运动组合影响的期权定价问题,而文献[2]研究的是风险证券价格受多个分数布朗运动影响的期权定价问题.本文研究的出发点结合了前人研究欧式期权定价问题的思想:考虑风险证券价格受多个分数布朗运动与一个布朗运动组合影响的欧式期权定价问题.在第二章开始介绍了期权的基础知识,包括期权的基本概念,期权的种类和期权的功能特征.然后简单概述了随机过程的基础知识,包括分数布朗运动定义和伊藤随机过程的定义.以上这些基本概念的描述,主要是为学习第三章和第四章的内容做好铺垫.第三章是本文的重点内容,研究的是风险证券价格受多个分数布朗运动与一个独立的布朗运动的线性组合影响的欧式期权定价模型.对于此类欧式期权定价模型有如下假设:(1)风险证券的价格变动是连续的且遵循几何布朗运动;(2)无风险利率是已知的且不随时间的变化而变化;(3)讨论了风险证券在不支付红利和支付红利的情况下的价格;(4)风险证券市场没有摩擦且没有卖空限制;(5)风险证券可以无限细分且能够自由买卖.第四章是在研究完第三章的基础上进行的.首先概述了幂期权的基础知识,使得人们对幂期权的内容和结构有更直观的了解.然后主要讨论了风险证券受多个分数布朗运动与一个独立的布朗运动的线性组合影响的欧式幂期权定价问题:在风险中性概率测度下,得出了在有红利支付的情况下红利率及无风险利率为非随机函数的两类欧式幂期权定价公式,并分别求出了涨跌欧式幂期权的平价关系.第五章是对本文的总结及对未来期权问题研究的展望.
[Abstract]:In this paper, we consider two options pricing problems in which the price of risky securities is affected by the combination of multiple fractional Brownian motions and one Brownian motion: the European option pricing problem under mixed fractional Brownian motion and the mixed fractional Brownian motion ring. The pricing problem of European power options in the world. First of all, in the first chapter, this paper introduces the research background of the current financial industry, and draws the conclusion that China has great potential in the field of financial derivatives in the future. Then, by introducing the emergence and development of option pricing theory, Can let people understand the development of options more intuitively, and provide a theoretical basis for the current study of options. In reference [1], we studied the option pricing problem of a portfolio of fractional Brownian motions and a Brownian motion, in which the price of risky securities is affected by one fractional Brownian motion. But in literature [2], we study the option pricing problem in which the price of risky securities is affected by multiple fractional Brownian motions. The starting point of this paper is combined with the thought of previous studies on European option pricing: considering the high price of risk securities. In chapter 2, we introduce the basic knowledge of options, which are affected by the combination of fractional Brownian motion and a Brownian motion. Including the basic concepts of options, types of options and options. Functional features. Then a brief overview of the basic knowledge of stochastic processes, including the definition of fractional Brownian motion and the definition of Ito stochastic process. The third chapter is the main content of this paper, the study of risk securities price by multiple fractional Brownian motion and an independent. For this type of European option pricing model, it is assumed that the price changes of risky securities are continuous and follow the geometric Brownian motion. Known and not changing over time the price of risk securities without paying dividends and dividends is discussed. 4) there is no friction in the risk securities market and there is no limit to short selling. To be able to buy and sell freely. Chapter 4th is based on the third chapter. First, the basic knowledge of power options is summarized. Make man. We have a more intuitive understanding of the content and structure of power options. Then we mainly discuss the pricing problem of European power options affected by the linear combination of multiple fractional Brownian motions and an independent Brownian motion: in the wind. Under the measure of risk neutral probability, In this paper, two kinds of European power option pricing formulas are obtained, where the red interest rate and the risk-free interest rate are non-random functions under the condition of dividend payment. Chapter 5th is the summary of this paper and the prospect of future options research.
【学位授予单位】：广西师范学院
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;O211.6

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