分数布朗运动环境中基于风险偏好的几类期权的定价研究

发布时间：2018-01-02 23:38

本文关键词：分数布朗运动环境中基于风险偏好的几类期权的定价研究　出处：《湘潭大学》2012年硕士论文　论文类型：学位论文

【摘要】：期权最初出现在美国，20世纪70年代中期，它作为一种金融衍生工具应运而生。自产生至今约四十年时间里，各国研究人员们对期权理论和实践应用的探索不断发展更新。在这些研究方向中，期权的定价问题一直是金融数学研究的核心问题之一。随着金融市场的不断完善和发展，许多新型期权（也叫奇异期权）相继产生。为了更好地满足市场需求，相关学者们想方设法对这些新型期权进行尽量客观的定价，以使得这些期权理论越来越趋近于真实市场情形。本文利用新的关于分数布朗运动的随机积分理论，运用测度变换以及条件分布，研究了在基于风险偏好的分数布朗运动环境中的幂型期权、重置期权和复合期权的定价问题。第一章主要是对期权的历史和研究现状做一简单介绍。第二章主要探讨的是分数布朗运动环境中基于风险偏好的幂型支付欧式期权在期满前任意时刻的定价。第三章主要是对基于风险偏好的、在分数布朗运动环境中的单时点重置欧式期权的定价公式进行了推导。第四章着重分析了在风险偏好下、分数布朗运动环境中的混合期权的定价，并且推导出了其在期满前任意时刻的定价公式。第五章总结本篇文章的主要结果、结论，，并依次提出几点在本文议题基础上引发的值得探讨的想法。
[Abstract]:Option first appeared in the United States in the middle of 70s, it emerged as a financial derivative. It has been around 40 years since it came into being. Researchers from all over the world are constantly developing and updating their exploration of options theory and practical application. In these research directions. Option pricing has always been one of the core problems in financial mathematics. With the continuous improvement and development of financial market, many new options (also called strange options) have emerged in order to better meet the market demand. The scholars try their best to price these new options objectively, so that the theory of these options is more and more close to the real market situation. In this paper, we use the new stochastic integral theory about fractional Brownian motion, measure transformation and conditional distribution to study the power option in the environment of fractional Brownian motion based on risk preference. The pricing of replacement option and compound option. The first chapter is a brief introduction to the history and research status of options. In the second chapter, we mainly discuss the pricing of power-type payment options based on risk preference in fractional Brownian motion environment at any time before expiration. In the third chapter, the pricing formula of single-point reset European option in fractional Brownian motion is derived based on risk preference. Chapter 4th focuses on the pricing of mixed options in fractional Brownian motion under risk preference and deduces its pricing formula at any time before expiration. Chapter 5th summarizes the main results and conclusions of this paper, and puts forward some ideas which are worthy of discussion on the basis of this paper.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;O211.6

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