【作者】 张辉；

【导师】 孔繁亮；

【作者基本信息】 哈尔滨理工大学 ， 应用数学， 2008， 硕士

【摘要】 障碍期权(又称关卡期权)是一种受一定限制的特殊期权,其期权的最终收益不仅依赖于原生资产在期权到期日的价格,而且与在期权有效期内原生资产价格是否达到某个(或几个)合约规定的水平有关,故其定价比标准的欧式期权复杂,但对其投资具有风险低和成本低的特点,所以受到了市场的青睐,其定价问题是当前金融统计学面临的重要研究课题之一。本文从期权定价理论的研究背景出发,在分析了期权的基本概念、内容、方法基础上,研究了期权的一般定价方法,讨论了B-S期权定价方程。将鞅分析的思想方法引入到期权定价中去,在分析了鞅的基本概念、基本理论、近年来的发展状况的基础上,用鞅分析的方法对关卡期权的定价进行了分析与探讨。《期权定价的数学模型和方法》一书是在建立关卡期权的偏微分方程模型的基础上,通过解带有边界条件的偏微分方程求解,过程复杂。应用等价鞅测度,探讨贴现后的股票价格过程,定价关卡期权起到了简化定价过程的作用。并利用鞅分析的方法进一步讨论了加入异常波动的关卡期权的定价问题,通过实证分析比较了传统的对数正态分布模型和波动源模型两种股价波动模型,得出波动源模型能更实际、更精确的描述股价波动,从而对期权定价起到了指导性的作用。本文用鞅分析的方法得出了期权定价的表达式,这不仅丰富了鞅的应用,而且在金融统计中,具有实际意义。更多还原

【Abstract】 Barrier option is a kind of limited options. The final income of the kind of options not only depends on the original asset price in the option expire but whether the original asset price attains prescriptive price in term of option validity is related. So its pricing is more complicated than European option. But the investment of Barrier option is low-risk and low- cost. And it is favored by market. The pricing of the Barrier option is one of the most important questions in financial statistics.In this paper, we research background of option pricing theory, Based on the concepts, contents and methods of option, general option pricing method and B-S option pricing function are discussed to illuminate hedge thoughts.Martingale analysis is applied to option pricing. Based on the fundamental concepts and theories, developments in recent years of martingale, Barrier option pricing is discussed by martingale analysis. It is pricing Barrier option by solving partial differential equation with boundary conditions in Mathematics model and method of option pricing. That process is complicated. But discussing discounted stock price by equivalent martingale measure and pricing Barrier option with martingale analysis and stochastic process simplified the pricing process. On the basis of the research of the former, The pricing of Barrier option added abnormal fluctuation is discussed. Finally, we make a contrast between traditional lognomality model and fluctuating sources model through empirical analysis, it shows that fluctuating sources model can describe the real stock market more practically and accurately than the traditional lognomality model, so the pricing of option in fluctuating sources model has guiding action .we obtain formulation of option pricing by martingale analysis, which is not only valuable to rich application of martingale theory, but also practical to financial statistics.更多还原