美式勒式期权定价研究
发布时间：2018-10-21 18:25
【摘要】：本文主要研究在常数波动率与随机波动率下一维与多维美式勒式期权的定价问题。欧式的勒式期权相当于一个欧式看涨期权和一个欧式看跌期权的组合,而美式的勒式期权由于其提前执行的特性,导致了其价值与最佳实施边界不同于一个美式看涨期权和一个美式看跌期权的组合,并且迄今为止,对美式勒式期权的研究还不充分。由于美式期权可在到期日前任意时刻实施,导致其定价不像欧式期权一样存在一个显式定价公式,因此需要使用数值方法求解。本文使用了叉树方法和最小二乘蒙特卡洛方法计算常数波动率和随机波动率下的一维和多维美式勒式期权,并且给出了其最佳实施边界。 首先,本文阐述了选题背景和意义。美式期权由于其可提前执行的特点,成为金融市场中最活跃的期权交易类型。在美式期权这一类型中涌现了大量的交易品种,如亚式,回望式,蝶式,勒式等。其中美式勒式期权由于还未开始交易,因此相关研究文献比较少。但是美式勒式期权其适合新兴金融市场的特点在未来的应用前景必然十分广泛,欧式的勒式期权(勒式组合)已经成为期权交易者的必备策略之一,美式勒式期权的产品研发上市只是时间的问题。研究美式勒式期权的定价问题,无论在交易市场上还是学术上,都非常有意义。本文希望能够通过研究,丰富对勒式期权的认识,为期权研究做出一些贡献。 其次,本文核心内容可分为三个部分,第一部分为常数波动率下的美式勒式期权的定价研究,第二部分为随机波动率下的美式勒式期权的定价研究,第三部分为多维美式勒式期权的定价研究。 最后,本文给出了结论以及对文章进一步研究的展望。
[Abstract]:In this paper, we study the pricing of one-dimensional and multi-dimensional American-type options under constant volatility and stochastic volatility. The European option is equivalent to the combination of a European call option and a European put option, while the American Le option has the characteristics of early execution. It leads to the difference between the value and the optimal implementation boundary of an American call option and an American put option, and so far, the research on the American Le option is not sufficient. Because the American option can be implemented at any time before the expiration date, the pricing of American option does not have an explicit pricing formula as that of European option, so it needs to be solved by numerical method. In this paper, the cross tree method and the least square Monte Carlo method are used to calculate the one dimensional multi dimensional American type option with constant volatility and random volatility, and the optimal implementation boundary is given. First of all, this paper expounds the background and significance of the topic. American option has become the most active option trading type in financial market because of its characteristics of early execution. A large number of American options have emerged in this type of trading, such as Asian, looking back, butterfly, and so on. Among them, the American-type option has not started trading, so the relevant research literature is relatively few. However, the characteristics of American type options which are suitable for emerging financial markets will be widely used in the future, and the European type of Le options has become one of the necessary strategies for option traders. It is only a matter of time before the R & D of American-style options is listed. It is very meaningful to study the pricing of American-type options both in the trading market and academically. This paper hopes to enrich the understanding of Le options and make some contributions to the study of options. Secondly, the core content of this paper can be divided into three parts: the first part is the pricing research of American type option under constant volatility, the second part is the study of American type option pricing under random volatility. The third part is the pricing of multi-dimensional American-type options. Finally, the conclusion and the prospect of further research 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】：2012
【分类号】：F830.9;F224
本文编号：2285967
[Abstract]:In this paper, we study the pricing of one-dimensional and multi-dimensional American-type options under constant volatility and stochastic volatility. The European option is equivalent to the combination of a European call option and a European put option, while the American Le option has the characteristics of early execution. It leads to the difference between the value and the optimal implementation boundary of an American call option and an American put option, and so far, the research on the American Le option is not sufficient. Because the American option can be implemented at any time before the expiration date, the pricing of American option does not have an explicit pricing formula as that of European option, so it needs to be solved by numerical method. In this paper, the cross tree method and the least square Monte Carlo method are used to calculate the one dimensional multi dimensional American type option with constant volatility and random volatility, and the optimal implementation boundary is given. First of all, this paper expounds the background and significance of the topic. American option has become the most active option trading type in financial market because of its characteristics of early execution. A large number of American options have emerged in this type of trading, such as Asian, looking back, butterfly, and so on. Among them, the American-type option has not started trading, so the relevant research literature is relatively few. However, the characteristics of American type options which are suitable for emerging financial markets will be widely used in the future, and the European type of Le options has become one of the necessary strategies for option traders. It is only a matter of time before the R & D of American-style options is listed. It is very meaningful to study the pricing of American-type options both in the trading market and academically. This paper hopes to enrich the understanding of Le options and make some contributions to the study of options. Secondly, the core content of this paper can be divided into three parts: the first part is the pricing research of American type option under constant volatility, the second part is the study of American type option pricing under random volatility. The third part is the pricing of multi-dimensional American-type options. Finally, the conclusion and the prospect of further research 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】：2012
【分类号】：F830.9;F224
【参考文献】
相关期刊论文 前1条
1 邓东雅;马敬堂;单悦;;美式勒式期权定价问题研究[J];南方金融;2011年12期
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