导　　师： 王晓天

学科专业： 070103

授予学位： 硕士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 经典的Black-Scholes期权定价公式是在一系列严格的假设下获得的,而这些假设与实际金融市场的运行规律并不一致,其定价结果并不十分理想。因此,适当放松Black-Scholes期权定价模型的假设,得出能揭示实际金融市场运行规律的期权定价公式是数理金融研究的热点问题,也是本文研究的主要问题。 本文首先给出了研究背景和选题意义、文献回顾和研究现状。其次简单地回顾了本论文研究所用的随机过程和行为金融方面的预备知识,并介绍了主要的两资产期权及其在经典Black-Scholes模型下的定价公式。 本文的主要结果为：根据行为金融学的观点,在投资者有限理性的假设下用分数Brown运动代替了经典Black-Scholes模型中的Brown运动、估计股票价格服从的概率分布时用锚定-调整策略取代了Bayes定理、Taylor公式取代了连续交易环境下的Ito公式,解决了离散场合分数Black-Scholes模型下带交易费用的两资产期权定价问题。关于这一问题的研究,目前尚未见到类似的研究报告。通过在离散场合下对平均自融资Delta对冲策略的讨论,我们用近似规避的方法获得了两资产期权价格满足的微分方程。作为这个微分方程的运用,我们得到了交换期权、择好期权和超额表现期权的定价公式。进而,我们还得到了最优的交易时段间隔及在最优的交易时段间隔下的上述三种期权的最小值。事实上,这些最小值就是上述三个期权的上规避价,可以看做是它们的实际价值。此外,通过讨论得出标度和长期依赖性对期权价格有着十分重要的影响。 Classic Black-Scholes option pricing formula is built on a series of strict assumptions。These assumptions are not consistent with the actual operation law in the real financial market, so the pricing results were not ideal when using Black-Scholes option pricing formula in practice. Therefore, relaxing the assumptions of the Black-Scholes option pricing model to get the option pricing formula which can reveal the actual operation rules in the real financial market is the hotspot in mathematical financial research, and is also the main problem in this paper. This paper first reviews systematically the research on option pricing. Then briefly introduced the useful knowledge of Random process and Behavioral finance, and presented the main two-asset options and their pricing formulas in the classic Black-Scholes model. The main results are in the following:according to the points of Behavioral finance, under the hypothesis of bounded rational investors we replaced the standard Brownian motion by the fractional Brownian motion in the classical Black-Scholes model, anchoring-adjustment by the Bayes theorem when estimating the probability, Taylor's formula by Ito formula in the continuous trading environment, and we solved the problem of discrete-time two-asset option pricing by the fractional Black-Scholes model with transaction costs. About this problem, we has not yet seen the similar papers at present. By a mean-self-financing delta-hedging argument in a discrete time setting, a two-asset option pricing differential equation is obtained. As an application of it, we get the pricing formulas of exchange option, outer performance option and better-of option. Furthermore, the minimal prices of these three options under transaction costs are obtained. In fact, these minimal prices are the super-hedging prices which can be used as the actual prices of them. In addition, we also know that scaling and long-range dependence have a significant impact on option pricing.

关 键 词： 对冲 瞄定 调整 交易费用 两资产期权定价 标度

分 类 号： [F224 F830.9]

领　　域： [经济管理] [经济管理]