对数t分布下带跳的回望期权定价

发布时间：2019-04-16 21:04

【摘要】：经典的Black-Scholes期权定价公式是以Brown运动作为驱使噪声的，但大量的实证研究表明，股票收益率的密度函数呈现高峰厚尾特征．为此，研究者们建立了股票收益的双曲分布、Pareto分布、t分布和随机波动模型以尽可能地反映市场股价的真实动态．实证研究发现t分布模型尤其适合股票对数收益的分布．因此，，研究t分布模型下的期权定价问题具有重要的理论与现实意义．回望期权是金融机构设计出的交易方式更方便更灵活和交易价格更合适的新型期权中的一种，它的收益对标的股票在期权有效期内价格动态的依赖是很强的，是强路径依赖期权的一个典型品种，对该期权进行详细的理论研究具有十分重要的意义．本文主要研究了对数t分布下带跳的回望期权定价的相关问题．本文的核心部分在第三章和第四章．第三章主要研究了对数t分布下带跳的回望期权定价问题，其方法分为三个步骤：（1）结合行为金融相关理论提出模型的假设，用条件Delta规避方法推导出期权价格满足的偏微分方程，并得出了回望期权的理论价格．（2）用最小均方误差规避方法得到回望期权市场价格的闭型解，这和行为金融中资产价格具有均值回归的观点相一致．（3）提出基于风险价值(VaR)的波动率参数σ估计的新方法，该方法可使定价误差和投资者的风险偏好相一致．第四章研究了对数t分布下浮动执行价格和固定执行价格回望期权之间的关系．本文的创新之处有：（1）全面的研究了对数t分布下带跳的回望期权定价问题．（2）在标度不变性的基础上提出局部信息假设．（3）提出最小均方误差规避方法，得到对数t分布下带跳的回望期权市场价格的闭型解．（4）提出了基于风险价值（VaR）的波动率参数σ估计的新方法．（5）详细给出了浮动执行价格和固定执行价格回望期权之间的关系．
[Abstract]:The classical Black-Scholes option pricing formula is driven by the Brown motion. However, a large number of empirical studies show that the density function of the stock return has the characteristics of peak thick tail. Therefore, researchers have established the hyperbolic distribution of the stock return. The Pareto distribution, t distribution and random fluctuation model can reflect the real dynamics of stock price as much as possible. The empirical study shows that the t distribution model is especially suitable for the distribution of logarithmic returns of stocks. It is of great theoretical and practical significance to study the option pricing problem under t-distribution model. Look back option is one of the new options designed by financial institutions, which is more convenient, more flexible and more suitable for trading price. Its return is strongly dependent on the price dynamics of underlying stocks during the term of the option, and is a typical variety of strongly path-dependent options. A detailed theoretical study of this option is of great significance. In this paper, we mainly study the pricing of forward-looking options with jump under logarithm t distribution. The core part of this paper is in chapters 3 and 4. In the third chapter, we mainly study the pricing problem of looking back options with jump under logarithm t distribution. The method is divided into three steps: (1) based on the theory of behavioral finance, the hypotheses of the model are put forward, and the partial differential equation of option price satisfaction is derived by conditional Delta avoidance method. The theoretical price of the look-back option is obtained. (2) the closed-form solution of the market price of the look-back option is obtained by the method of minimum mean square error avoidance. This is consistent with the view that asset price has mean regression in behavioral finance. (3) A new method for estimating volatility parameter 蟽 based on value-at-risk (VaR) is proposed. This method can make the pricing error consistent with the investor's risk preference. Chapter 4 studies the relationship between floating execution price and fixed execution price look-back option under logarithm t distribution. The innovations of this paper are as follows: (1) the pricing problem of looking back options with jump under logarithm t distribution is studied comprehensively. (2) based on the scale invariance, the local information hypothesis is proposed. (3) the minimum mean square error avoidance method is proposed. In this paper, we obtain the closed-type solution of the market price of look-back options with jump under logarithm t distribution. (4) A new method for estimating volatility parameter 蟽 based on value-at-risk (VaR) is proposed. (5) floating ideation is given in detail. The relationship between the line price and the fixed execution price look back option.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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