离散模型下两种新型期权的定价研究

发布时间：2018-01-07 12:18

本文关键词：离散模型下两种新型期权的定价研究　出处：《华中师范大学》2013年硕士论文　论文类型：学位论文

【摘要】：期权是指持有者在支付一定的期权费之后所获得的一种买卖一定标的资产的权利。近年来,期权做为一种防范风险或投机的手段得到迅速发展。由于在期权合约签订后,期权的价格会随着市场供求变化等信息的出现而发生变化,并且直接决定投资者的盈亏,因此期权定价问题是期权交易的核心。为了满足日益变化的市场投资需求,各种具有不同特点的新型期权被设计出来,其中障碍期权和回望期权就是比较常见的两种新型期权。传统B-S模型下期权的定价要求在连续时间模型下进行,而实际中大量期权定价问题是在离散模型下考虑的。对于障碍期权和回望期权,它们路径依赖性的特点使得在实际中的期权价格与连续模型下定价公式计算出的期权价格之间存在明显差异,所以障碍期权和回望期权在离散模型下的定价研究就显得比较重要。本文主要研究的是离散时间模型下障碍期权和回望期权的定价问题,给出了障碍期权和回望期权分别在离散和连续模型下定价之间的关系。对于障碍期权,通过Girsanov定理和反射原理等组成的新方法,求出离散模型下单障碍期权的定价表达式,将其与连续模型下障碍期权的定价公式相比较,从而得出两者之间的关系；接着将这种关系式推广到另外一种链式的双障碍期权上。另外一方面,对于回望期权,在B-S模型下回望期权在离散和连续模型下定价关系的基础上,通过将布朗运动极值定理推广到一般的跳扩散模型中,得到跳扩散模型下回望期权在离散和连续模型下定价之间的关系。
[Abstract]:Option refers to the sale of a holder obtained after paying a certain fee options the underlying asset rights. In recent years, the rapid development of the option as a means to avoid risk or speculation. Since the signing of the options contracts, the price of an option will appear along with the changes of market supply and demand information changes, and directly determine the investor's profit and loss, so the problem of option pricing is the core trading options. In order to meet the ever-changing market demand for investment, new options with different characteristics were designed, including two new options, barrier options and lookback options is relatively common. The traditional B-S model option pricing requirements in continuous time model, and a large number of real option pricing problem is considered in the discrete model. The barrier options and lookback options, they are path dependent. There is a significant difference between the option price in real and the option price calculated under the continuous model, so the pricing of barrier options and look back options in discrete models is more important.
This paper mainly studies the problem of pricing barrier options and lookback options with discrete time model, given the relationship between the barrier options and lookback options pricing respectively in discrete and continuous models. For barrier options, a new method of using the Girsanov theorem and the principle of reflection etc., calculate the pricing formula of discrete model single barrier option and the formula of option pricing model under continuous barriers compared to draw the relationship between the two; then this relation is extended to another chain of double barrier option. On the other hand, the lookback option, under the B-S model of option pricing in discrete and continuous models on the basis of the relationship between Brown, the movement of extreme value theorem is extended to the jump diffusion model, jump diffusion relationship between the lookback option model in discrete and continuous pricing model.

【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

【共引文献】