【作者】 韩师文；

【导师】 柴俊；

【作者基本信息】 华东师范大学 ， 应用数学， 2010， 硕士

【摘要】 期权作为二十世纪金融行业创新的一个代表产物,在1973年的美国芝加哥期权交易所第一次开始交易后,对于整个金融衍生品市场及金融数学理论所带来的冲击是当时无人所能预想到的。现今,期权交易市场已经成为整个金融市场里不可或缺的一个重要组成部分。基于以上原因,对于期权定价理论与实证的研究推动了金融创新的新高潮。本文主要介绍一种新型的重设期权,并且结合概率论中的鞅理论、随机微分方程、测度论等数学工具,对于该期权在风险中性概率测度下的理论公允价格给出了多重积分形式的表达式。对于这一新型期权,即多点重设期权,是在前人对于标准重设期权讨论的基础上,进行了创新,在原有的重设方案的基础上,多加了一层重设。这样的创新主要是受到了可转换债券的启发：由于可转债一般会有这样的规定,在一段时间内股价不超出某一限制则允许进行转换。本文将这一规定进行了一定修正后加入重设规则的构建中,使得重设条件与股价在一段时间内的最大值有关,如果股价在这一段持续的时间内超过一定水平则将取消重设资格。与原先只以某一时刻的价格水平来决定是否进行重设的方案相比,新型期权的设计大大降低了投机者利用原来单一的重设结构来操作股价,乘机套利的机会。本文的研究目标也对于这样的期权采用风险中性条件下,等价鞅测度变化的方法给出其理论公允值。这种新型期权突破原来重设期权的固有方式,在求解上也要借助一些复杂的随机微分方程理论,利用原生资产首达时间的概率密度函数,反复利用联合概率分布和条件概率的乘法公式进行计算,做了具有一定原创性的工作。更多还原

【Abstract】 "Option" is considered to be a successful example of creative practice world finance market of the 20th Century. Although options have been firstly traded in American Chicago Board Option Exchange since 1973, almost nobody could, at that time, foresee that they would bring about huge influence on practice and financial and banking theory in the following several decades. Now option market has become an important part of international finance market. Under such background, research and application of option pricing theory, currently, set off a new climax of innovation in the field of financial theory.A new kind of reset option will be introduced in this paper, and we are going to give out the expression in multi-integration form with the method of martingale theory and stochastic analysisThis new kind of option, single point multiple level reset option, based on the research of the theory before, I constitute a brand new kind of reset option. Inspired by the convertible bonds’exchange regulation, a new stage of the reset is added to the option besides of the basic principle, which can be more helpful to prevent the arbitrage of the speculator controlling the asset price by means of great amount contract than the original reset option. The aim of our research is actually to show the fair price of the option in the risk neutral probability measure with Girsanov theorem. The new option just break the ordinary thought of the reset option, and much knowledge of stochastic differential equation and the Multiplication Formula in probability space will be necessary for solving the pricing problem, setting out some creative work.更多还原