【作者】 李小红；

【导师】 何穗；

【作者基本信息】 华中师范大学 ， 应用数学， 2008， 硕士

【摘要】 近年来,随着金融市场需求复杂程度的提高,仅仅使用标准期权已很难满足市场的需要,为了满足市场及某些客户的特殊需求,许多金融公司除了提供人们广为熟悉的欧式、美式期权外,还设计了大量由标准期权衍生的通常在场外市场交易的新品种—非标准化的衍生证券,我们称其为新型期权(Exotic Options)。新型期权中大多都具备路径依赖特征,即期权价格不仅取决于其到期日标的资产价格,而且取决于标的资产价格在期权有效期内的变化路径,亚式期权(Asian Options)正是其中的一种代表性的产品,同时它也是当今金融衍生品市场中最为活跃的一种新型期权,由于具备路径依赖特征,使得亚式期权的定价模型与标准期权的定价模型相比呈现出比较大的差异,其定价问题远比欧式期权定价复杂。本文主要研究新型期权中的亚式期权,它是强路径依赖型期权的典型代表,亚式期权与标准期权明显不同,它实质上是欧式期权的一种创新,因此它与标准欧式期权有着密切的联系,所以溯根求源,在B-S模型的基础上来展开本文的研究工作。本文给出了一个强依赖期权统一的Black-Scholes模型。由于路径依赖期权的独有的路径依赖特征,我们引入一个路径因子,并利用It(?)定理与无套利原理推导出强路径依赖期权统一的B-S模型,对应不同的路径函数,只需在统一模型的基础上给出具体的路径函数,再结合其相应终值条件和所带有的一些边界条件,就可以通过求解方程得到定价公式。另外,利用强路径依赖期权统一的B-S模型得到了连续情形下固定敲定价格和浮动敲定价格的几何平均亚式期权的定价结果及在非风险中性世界中连续情况下具固定敲定价格的几何平均亚式期权的定价公式。更多还原

【Abstract】 In recent years, along with the improvement of demand on the complexity in money market, it is difficult to satisfy the special needs of customers by only using the standard option. In order to satisfying the demand of markets and customers, many financial companies not only designed European options and American options but also devised a great deal of new breeds which derive from standard options and exchange out of the counter commonly. We call it exotic options. Most of exotic options possess the feature of path-dependent, that is to say, the option price not only depends on the option price at maturity; but also depends on varying of the underlying assets price. Asian options are just one of the typical products, and it is a kind of exotic options which is the most active one in financial derivative markets. Because of the property of path-dependent, there exists distinguished difference between Asian option pricing model and standard options.The main goal of this paper is to study Asian options. It is a typical representative of strongly path-dependent options, Asian option is different from standard option obviously. It is innovation of European options. So it connects with the standard European options nearly. Black-Scholes Option Pricing Model is just one of the most effective means to solve main content of the article. Therefore we should understand Black-Scholes Option Pricing Model fully which concludes to our research.This paper gives the uniform Black-Scholes Model of strong path-dependent options.Because of the unique character of path-dependent options, we import a path-factor, then deduce the uniform B-S Model of strong path-dependent option using Ito theory and no-arbitrage principle. For different path-factor, with a concrete path function, initial condition and boundary condition we can get the pricing formula on solving the equation. In addition, we get the price of geometric average Asian option with fixed strike price and floating strike price, making use of the uniform B-S Model of strong path-dependent option and the pricing formula of geometric average Asian options under no risk-neutral world.更多还原