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： 经典期权定价理论是建立在有效市场假设基础之上,即市场是无套利的、对数股票价格经过无风险利率折现服从一个鞅过程;这暗示在大多数场合股票价格增量应该是相互独立的。然而,实证分析及行为金融学的研究结果显示:股票价格收益具有长期依赖性及动量效应—即股票价格的增量不具有独立性而具有正的自相关性。因此我们有必要研究股票收益具有长期依赖性及动量效应时的期权定价问题。 实证分析显示,混合分数布朗运动可以很好的拟合股票收益的长期依赖性及动量效应。基于行为金融的观点,本文给出了在离散时间场合和混合分数布朗运动模型下带交易费的亚式期权定价公式。 亚式期权作为金融衍生品市场上交易最为活跃的奇异期权之一,在现实金融市场中得到广泛应用。它是一种路径依赖型期权,它在到期日的收益依赖整个期权有效期内标的资产价格的平均值,由于具有路径依赖特征,所以使得亚式期权定价比标准期权定价更为复杂。 基于行为金融学的锚定及调整启发式,本文通过运用Delta规避策略及平均自融资策略,给出了混合分数布朗运动模型下带交易费的亚式期权定价公式;所得结果显示时间标度δt及股票收益的长期依赖性对期权定价有重要影响。特别地,数值分析结果显示即使δt充分小,离散时间交易与连续时间交易也存在着本质不同;连续时间交易假设将导致期权值被低估。本文包括以下内容: 第一章是全文的引言部分,阐述了本文的研究背景与课题进展情况,简要的介绍了亚式期权和分数布朗运动的一些基本概念,以及本文涉及到的一些行为金融理论知识。 第二章比较详细地介绍了支付交易费的欧式期权定价模型,首先回顾对经典Black-Scholes模型推导过程,再对有交易成本的期权定价模型进行了比较全面的综述。 第三章是本文的核心部分,系统地推导了支付交易费的亚式期权定价公式。通过运用离散时间下平均自融资和Delta对冲策略得出几何亚式期权定价公式。结果显示时间标度δt与Hurst指数在存在交易费的情况下对期权定价起着重要作用。 第四章是本文的实证部分,通过数值分析得出标度与长记忆性对期权定价的影响。结果显示即使δt充分小,离散时间交易与连续时间交易也存在着本质不同。 Classic option pricing theory is built on the basis of efficient market hypothesis, that market has no arbitrage, logarithm stock price after a discount of risk-free rate follows a martingale process; this suggests the stock price increments in most cases should be mutually independent. However, empirical analysis and behavioral finance research results display: the stock returns have long-range dependence and momentum effect-the stock price increments are not independent and has a positive autocorrelation. Therefore it is necessary for us to study the option pricing problem when the stock returns have long-range dependence and momentum effect. Empirical analysis shows Brownian-fractional Brownian model can fit the long-term dependence and the momentum effects of stock returns well. Based on behavioral finance point of view, this paper gets an Asian option pricing formula under the mixed Brownian-fractional Brownian model with transaction costs in the discrete time setting. As one of the most active exotic options, Asian-style option is widely used in the financial market. It is a path-dependent option whose payoff depends on the average of underlying asset price over some pre-set period of time, and it is more complicated to price Asian-style option than standard options because of the path-dependence. Based on the anchoring and adjustment heuristic in behavioral finance, this paper obtains an Asian option pricing formula under the mixed Brownian-fractional Brownian model with transaction costs in the discrete-time trade setting by a mean-self-financing Delta-hedging argument; results show that time scalesδt and long-range dependence of stock returns play an important role in option pricing with transaction costs. In particular, the numerical results display that there exists fundamental difference between continuous-time trade and discrete-time trade even ifδt is small enough. This paper contains the following contents: The first chapter, as the introduction of this paper, describes the study background and the progress, briefly introduces some of the concepts of the Asian option and fractional Brownian motion, and some of the behavioral financial theory involved in the paper. The second chapter describes the option pricing model with transaction costs in more detail. First, we review the deduction process of the classic Black-Scholes model, and then we make a more comprehensive review to the option pricing model with transaction costs. The third chapter is the core of this paper, in which we deduce formula of Asian option pricing models with transaction costs systematically. By a mean-self-financing Delta-hedging argument in a discrete time setting, a geometric average Asian call option pricing formula is obtained. We show that time scalesδt and Hurst exponent H play an important role in option pricing with transaction costs. Chapter IV is the empirical part, we obtain how scaling and long-range dependence affect option pricing by numerical analysis. Results display that there exists fundamental difference between continuous-time trade and discrete-time trade even ifδt is small enough.

关 键 词： 锚定 调整 交易费 混合分数布朗运动模型 对冲 标度

分 类 号： [F224 F830.91]

领　　域： [经济管理] [经济管理]