随机波动率下美式期权的简单迭代法

发布时间：2018-01-13 04:35

本文关键词：随机波动率下美式期权的简单迭代法　出处：《西南财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文的目的是为了求解随机波动率下美式期权的定价问题。由于美式期权可在到期日前任一时刻实施,导致其定价不像欧式期权一样存在一个显式定价公式,而是在欧式期权价格的基础上再加上提前执行溢价(Early Exercise Premium,简称EEP)。EEP可以表示为一个包含自由边界,即最佳执行边界的积分式,当美式期权的价格落在该边界上时,执行这一期权的收益应等于该期权的价值。如果EEP的具体表达形式是已知的,那么从美式期权的定价公式中就可以推导出关于最佳执行边界的方程式。从这一方程式出发,通过某些数值方法,可以模拟得出自由边界。美式期权的最佳执行边界一旦得到确定,那么其定价问题也将迎刃而解。我们把以上求解自由边界的过程称为EEP简单迭代法。关于常数波动率下美式期权定价问题的EEP简单迭代法已经由Kim(2012)给出。本文的核心工作,是用EEP简单迭代法求解一种随机波动率下的美式期权最佳执行边界的问题。首先,本文阐述了选题背景。期权交易在当今金融市场中日益频繁,因为美式期权可在其执行时间段内任意择时执行的特点,使之优于欧式期权而被广泛使用。但正是因为美式期权执行时间的不确定性,使之价格无固定公式可依,导致其定价问题成为学术界研讨热点。因此,研究美式期权的定价问题,无论在实用上还是学术上,都非常有意义。其次,本文回顾了常数波动率下美式期权定价的EEP简单迭代法。回顾的目的有两方面：一是使读者了解本文大量使用的理论基础和研究方法；二是为使本文的结构更加连贯,起到层层深入的效果。再次,提出本文的核心部分,用EEP简单迭代法求解随机波动率下美式期权的定价问题。此部分指出美式期权定价在随机波动率和常数波动率下的不同之处后,构造了EEP简单迭代,然后通过实证计算,肯定了研究方法的有效性。最后,本文给出了结论以及对后续工作的展望。
[Abstract]:The purpose of this paper is to solve the pricing problem of American options under random volatility. Because American options can be implemented at one time before the maturity date, there is not an explicit pricing formula for American options like European options. It is based on the European option price plus early Exercise Premium, or EEP).EEP, which can be expressed as a free boundary. When the price of the American option falls on the boundary, the proceeds of the option should be equal to the value of the option, if the specific expression of EEP is known. From the pricing formula of American option, we can deduce the equation of optimal execution boundary. From this equation, we can use some numerical methods. The free boundary can be obtained by simulation. Once the optimal executive boundary of American option is determined. Then the pricing problem will also be solved. We refer to the above process of solving the free boundary as EEP simple iteration method. The EEP simple iteration method for the American option pricing problem with constant volatility has been used by Kim. (. The core work of this paper is given. EEP simple iterative method is used to solve the optimal execution boundary of American option under random volatility. First of all, this paper describes the background of the topic. Option trading in the financial market is becoming more and more frequent, because American options can be carried out at any time in its execution period. It is more widely used than European option, but because of the uncertainty of American option's execution time, the price of American option has no fixed formula, so the pricing of American option has become a hot topic in academic circles. It is very meaningful to study the pricing of American option whether it is practical or academic. Secondly. This paper reviews the EEP simple iterative method for the pricing of American options under constant volatility. The purpose of the review is twofold: one is to make readers understand the theoretical basis and research methods used extensively in this paper; Second, in order to make the structure of this article more coherent, play layers of in-depth effect. Again, the core part of this paper. The EEP simple iteration method is used to solve the pricing problem of American option under random volatility. This part points out the differences between American option pricing under random volatility and constant volatility, and constructs a simple EEP iteration. Then the validity of the research method is confirmed by empirical calculation. Finally, the conclusion and the prospect of the future work are given.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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