【作者】 陈衡军；

【导师】 杨向群；

【作者基本信息】 湖南师范大学 ， 概率论与数理统计， 2008， 硕士

【摘要】 期权是一种有效的风险管理工具。随着金融理论的发展和市场的需求,人们在标准期权的基础上设计出新型期权,称为奇异期权(Exotic Option)。常见的有亚式期权、障碍期权、再装期权、经理人员股票期权、回望期权、重置期权。奇异期权大多具备路径依赖特征。比如亚式期权的收益就不仅取决于到期日的标的资产价格还与标的资产在有效期内的平均价格有关。从而使得奇异期权的定价比标准期权复杂。本文讨论亚式几何连续平均期权的定价。根据奇异期权各自的特点,将亚式期权与其它一些奇异期权组合,设计并得到了新型亚式几何连续期权,以满足市场和公司金融政策的具体需要。在标的资产服从指数O-U过程模型的假设下,利用Girsanov定理,构造了风险中性概率测度,应用随机分析的理论和工具,给出了一类亚式期权价格的显示表达式。本文主要工作如下:1、简化了亚式几何连续平均形式的表达式,用鞅方法推出了一般亚式期权定价公式,并讨论了看涨与看跌的平价关系。2、将亚式期权与障碍期权的特点联系起来,创造出一种新型亚式障碍期权,并给出期权定价的显式表达式。3、考虑到再装期权的特征,将亚式几何连续平均形式融入其中,并且进行了适当的变化,得到一种新型亚式再装期权,并推导出这种新型期权的定价公式。4、根据市场的需求和普通经理人员股票的不足,设计了一种新型亚式经理股票期权,并给出相应期权的显示表达式。更多还原

【Abstract】 Option is an effective tool of risk management.With the development of economy and demand of reset market,Some new type of options was designed from standard option,call it Exotic Options.We are Familiar with some exotic options ,such as Asian Options,Barrier Options,Reset Options,Executive Stock Option( ESO),Look-back Option,Reload Options.Most of all exotic options have characteristics of path-dependence.For example,the payoff of asian options depends not only on the maturity of the underlying asset price,but also some type average value of the underlying assets prices.So it is more complex to price the exotic options than standard options.in this dissertation we discuss the pricing problem of geometric continue averagerate asian option.We created some new forms of asian option which associated with some other exotic option and asian option based on the character of themselves. Under the hypothesis of the underlying assets are driven by exponential O-U process model,we constructed risk-neutral probability measure by using Girsanov theorem and obtained the pricing formulas of new type option which talked above by application of the theory and tools of stochastic analysis.In detail we have made works as follows:1、By skillful handled the form of geometric continue average-rate asian option, the pricing formula of the asian option was driven by using martingale method and put-call parity relation is deduced.2、Connected characteristic of asian option to barrier option,we created a new type of asian-barrier option and obtained pricing formula of the option.3、Thinking about the trait of reload option,we syncretized form of geometry continue average-rate into reload option and get a new type exotic option,and changed properly.The pricing formula is deduced.4、Based on demand of market and deficiency of executive stock option,we contrived a new type ESO which with asian option and obtained explicit expression of the new option.更多还原