导　　师： 郭艾

学科专业： 070104

授予学位： 硕士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 近年来,随着市场需求复杂程度的提高,仅仅使用标准期权已很难满足客户的特殊需要,金融机构为此设计了许多交易方式更灵活方便的期权,称为新型期权.亚式期权作为一种新型期权备受瞩目,但由于其强路径依赖性,其定价问题也相当复杂.因此,对其定价的研究也一直是个热门且非常有意义的课题.本文研究的是不完备市场中,当标的资产的价格出现不连续跳跃时,亚式期权的定价问题.全文共分四章. 第一章介绍了本文的研究背景、亚式期权定价的研究现状及期权定价的历史. 第二章介绍了期权和亚式期权的相关知识,以及与亚式期权定价相关的金融随机分析方面的知识. 第三章介绍了Kuan-Wen Chen和Yuh-Dauh Lyuu在完备市场中用价格下界定价亚式期权的思想,以及其对具有固定敲定价格的亚式期权和具有浮动敲定价格的亚式期权定价公式的具体推导过程和有关数值计算结果. 第四章是本文的主要部分.借鉴第三章中用价格下界定价亚式期权的方法,推导出当标的资产的价格服从跳跃-扩散模型时,具有固定敲定价格的亚式期权和具有浮动敲定价格的亚式期权的定价公式.本章首先根据亚式期权价格下界表达式的特点,选定一个特殊的集合,然后通过这样一个集合来求出亚式期权价格下界的最大值.最后,用Mathematica5.0对该下界进行数值计算,得到的数值结果与Monte Carlo模拟法求得的亚式期权的价格十分接近.故当金融市场上标的资产/(例如股票/)的价格出现“不正常”振动时,即可用本章推导的下界公式对亚式期权定价. In recent years, with the improvement of demand complexity in the market,only using standard options are hard to satisfy the special needs of customers, so the financial institution designs many options which have more flexible and convenient traded ways, they are called the exotic options. Asian options as a kind of exotic options are high-profile, but due to its strong dependence on the path, its pricing becomes quite complex. Therefore, the study on Asian options pricing has been a hot and very meaningful task. In this paper, we study the Asian options pricing in the incomplete market as the price of underlying asset varies with discontinuous jump. The paper is divided into four chapters. In the first chapter, we introduce the research background, the research status of Asian options pricing and the history of options pricing. In the second chapter, we introduce the relevant knowledge of options and Asian options, and the relevant knowledge of Asian options pricing in stochastic calculus applied to finance. The third chapter, we state the idea from Kuan-Wen Chen and Yuh-Dauh Lyuu that using the lower-bound formula of price to price Asian options in the complete market, and their specific derivation of the pricing formulas of Asian options with fixed strike price and Asian options with floating strike price. We also introduce their relevant numerical results. The fourth chapter is major component in this paper. Referencing the method that using the lower-bound formula of price to price Asian options in the third chapter, we derive pricing formulas of Asian options with fixed strike price and Asian options with floating strike price as the price of underlying asset follows the jump-diffusion model. In this chapter, we first according to the characteristic from the lower-bound expression of price of Asian options, choosing a special set that can find out the maximum of the lower-bound expression of Asian options. Finally, we use the Mathematica5.0 to calculate the lower-bound formula, we can find the numerical results approximate the prices of Asian options that are computed by Monte Carlo simulation method. Therefore, when the price of underlying assets /(such as stock/) appears 'abnormal' vibration in the financial market, we can use the lower-bound formulas derived in this chapter to price Asian options.

关 键 词： 亚式期权 定价公式 价格下界 跳跃 扩散

分 类 号： [F830.9 F224]

领　　域： [经济管理] [经济管理]