强路径依赖期权的定价研究

发布时间：2018-03-24 05:19

本文选题：回望期权　切入点：亚式期权　出处：《华中师范大学》2012年硕士论文

【摘要】：期权在国际金融衍生市场上发展迅速,近年来,出现了大量的奇异期权,强路径依赖期权就是其中之一。强路径依赖期权主要包括两类：回望期权和亚式期权。这类强路径依赖期权的收益既依赖于标的资产价格,又依赖于期权在整个或者部分期权有效期内的标的资产价格历程。本文介绍了基于B-S欧式期权定价模型推广下的几种模型：CEV模型、B-P混合驱动模型、CEV下且受B-P混合驱动模型。CEV模型中,标的资产价格的波动率不是常数,而标的资产价格的波动率弹性是常数；对于B-P混合驱动模型,考虑到了标的资产价格在服从几何布朗运动的同时,也可能会发生随机跳跃；CEV下支付红利且受B-P混合驱动模型,是对标的资产价格综合考虑了前面两个模型的情况。这三个模型,使得标的资产价格所遵从的随机过程更接近现实。作者在前人的研究基础上,综合研究了上述三种推广模型下的回望期权和亚式期权的定价问题,主要是采用无套利原理和风险中性定价,得到了在这几种模型下的回望期权和亚式期权的定价模型,并用二叉树期权定价模型研究了支付离散红利的算术平均亚式期权的数值解法。这样可以使我们更好地比较三种推广模型对期权定价的影响。
[Abstract]:Options have developed rapidly in the international financial derivatives market. In recent years, a large number of exotic options have emerged. Strong path-dependent options are one of them. Strong path-dependent options include two main types: the lookback option and the Asian option. The returns of these options are dependent on the underlying asset price. It also depends on the underlying asset price course of option in the whole or part of the period of validity of the option. This paper introduces several kinds of models based on B-S European option pricing model. The volatility of underlying asset price is not constant under B-P hybrid drive model. The volatility elasticity of the underlying asset price is constant. For the B-P hybrid drive model, it is considered that the underlying asset price may pay dividends under the stochastic jump CEV and be subjected to the B-P hybrid drive model, while the underlying asset price is moving from geometric Brownian motion to the geometric Brownian motion. These three models make the stochastic process of underlying asset price more realistic. On the basis of previous studies, the author synthetically studies the pricing problems of the lookback option and Asian option under the above three generalized models, which are mainly based on the no-arbitrage principle and risk-neutral pricing. The pricing models of the lookback options and Asian options under these models are obtained. The numerical solution of arithmetic average Asian option for discrete dividend payment is studied by using the binomial tree option pricing model, which enables us to better compare the effects of the three generalized models on option pricing.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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