Esscher变换与期权定价

发布时间：2018-01-10 10:28

本文关键词：Esscher变换与期权定价　出处：《湖南师范大学》2012年硕士论文　论文类型：学位论文

【摘要】：随着中国经济的腾飞,中国金融业也在市场改革和对外开放中蓬勃发展,期权交易作为金融市场最重要的交易手段之一,它在中国金融市场上发挥的作用也越来越大,那么期权定价的重要性也就毋庸置疑. 关于对期权定价的求解有着很多不同的方法,而由于鞅方法的简洁方便,利用鞅方法求解期权定价问题一直是人们研究的重点. Esscher变换是一个经典的精算学计算工具,但自1994年Gerber-Shiu将其由精算领域引入数理金融领域以来,由于其方法简单明了,应用范围广泛,能够很好地解决各类期权定价问题；同年他又引入了Esscher鞅测度,结合鞅方法能够得出一些复杂模型的期权定价的解. 本文在前人的基础上,对这两种方法进行了合理的提取,归纳,总结；从金融市场的角度综述了鞅的概念和性质,利用Esscher变换和鞅方法研究了多个期权定价模型,并对上述的两种方法采取了不同的模型进行对比,得出了各自方法的优劣性比较.最后利用Esscher鞅测度和鞅方法,计算出了几个特殊的由Levy过程驱动的期权定价模型的显示解.
[Abstract]:With the rapid development of Chinese economy, Chinese financial industry is booming in market reform and opening to the outside world. Option trading is one of the most important trading methods in financial market. As it plays an increasingly important role in China's financial markets, the importance of option pricing is beyond doubt. There are many different methods to solve the option pricing problem. Because of the simplicity and convenience of the martingale method, it is always the focus of people to solve the option pricing problem by using the martingale method. Esscher transform is a classical actuarial calculation tool, but since Gerber-Shiu introduced it into the field of mathematical finance in 1994, its method is simple and clear. It has a wide range of applications and can solve all kinds of option pricing problems. In the same year, he also introduced Esscher martingale measure, which combined with martingale method can obtain the option pricing solutions of some complex models. In this paper, on the basis of predecessors, the two methods of reasonable extraction, induction, summary; This paper summarizes the concept and properties of martingale from the perspective of financial market, studies several option pricing models by using Esscher transform and martingale method, and compares the two methods with different models. Finally, by using Esscher martingale measure and martingale method, the display solutions of several special option pricing models driven by Levy process are calculated.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F832.5

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