【作者】 李萍；

【导师】 王子亭；

【作者基本信息】 中国石油大学 ， 计算数学， 2009， 硕士

【摘要】 在经济全球化的背景下,金融在中国经济中的核心地位进一步凸现。金融问题,将是各国经济社会发展、改革、稳定必须谨慎处理的首要战略性问题,也将是世界大国间竞争博弈、展现实力的战略性新领域。期权作为金融市场中的衍生证券之一,其理论的研究,对于金融市场的发展和金融风险的防范有着极其重要的应用,在理论和实践上都有重要的意义。首先,文章对期权定价理论、金融风险的主要成果以及目前的研究热点进行了详尽的介绍,深入阐述了课题的现实意义。接着,介绍了期权的有关概念及相关性质,从有效市场理论优缺点出发,引出了基于非线性市场结构的分形市场理论,并与有效市场理论进行比较,介绍了布朗运动与分数布朗运动的定义及相关性质。其次,文章研究了标的资产服从分数布朗运动的分数随机微分方程解的一般形式及其基本性质、分数Black-Scholes公式、分数Black-Scholes微分方程以及其对应的推广形式,重点研究了基于分数布朗运动下的障碍期权定价和权证定价公式。再次,文章基于风险思想和分形市场的期权定价理论,综述性的介绍了风险价值(VaR)法和重标极差法(R/S)的基本原理、计算方法以及有关应用。最后,文章特别地结合当前形势,针对由美国次贷危机引发的尚未见底、仍在蔓延的国际金融危机。在汲取众多学者的优秀思想的基础上,借用数学的逻辑思维对美国次贷危机发生的原因和启示进行了深入思考。更多还原

【Abstract】 Against the backdrop of economic globalization, Finance being the core of the China’s economy became marked. Financial issues will be the primary strategic problem of economic and social development, reform, stability. It must be handled with careful. Options are derivatives of financial market.Its theoretical study are important in theory and practice.It has an extremely important application in the development of financial markets and preventing financial risks.First, The paper give a detailed introduction for the main results and current research focus of the option pricing theory, as well as financial risks.And expound the practical significance of the subject in depth. Then, The paper introduce the concept and nature of options. From the advantages and disadvantages of the efficient market theory(EMH),The fractal market hypothesis(FMH) which based on nonlinear market structure be introduced and be compare with the EMH. Then introduce the definition and nature of the Brownian motion and fractional Brownian motion.Next, The paper study the general form and basic properties of the subject of fractional stochastic differential equations, whose underlying assets subject to fractional Brownian motion.And study the fractional Black-Scholes formula, fractional Black-Scholes differential equations and their deduction. The paper focus on the study of the barrier option and warrant pricing formula under fractional Brownian motion.Again,The paper gives an overview of the basic principles, calculation methods an application of VaR and R/S,according to the idea of financial risks and the option pricing theory of fractal market.As we known,The international financial crisis,that caused by the US subprime mortgage crisis,is not yet bottomed out and still spreading. Finally, according to the current situation particularly,The paper consider the cause and revelation of international financial crisis in depth by mathematical logic and the excellent idea of many scholars.更多还原