永久百慕大期权定价的积分方程方法

发布时间：2018-01-11 08:32

本文关键词：永久百慕大期权定价的积分方程方法　出处：《西南财经大学》2012年硕士论文　论文类型：学位论文

【摘要】：最近几年,非标准的美式期权的定价被越来越多的学者进行研究。永久百慕大期权是一种没有到期日,只能在合约规定的一系列时点上选择是否行权的非标准美式期权。对于永久百慕大期权定价的研究现在还不是很多,并且现有的一些研究成果的算法精度都不高。由于永久百慕大期权具有一条最优执行边界,其求解极其复杂,在实际应用中人们常常用永久美式期权的最优执行边界替换永久百慕大期权的最优执行边界,但却从来没有人研究过该种替换是否有效。本文将采用高精度配置方法对永久百慕大期权的最优执行边界以及定价进行求解。通过高精度配置方法的运用,得到精度更高更可靠的永久百慕大期权的定价以及最优执行策略。并且通过与永久美式期权定价及最优执行边界进行算例比较,验证采取永久美式期权的最优执行边界替换永久百慕大期权的最优执行边界的有效性。本文首先介绍永久百慕大期权的概念及定价研究综述,以及永久美式期权及高精度配置方法。其次通过高精度配置方法对永久百慕大期权的最优执行边界以及定价积分表达式进行求解。接着通过MATLAB进行数值实现,研究永久美式期权与永久百慕大期权最优执行边界间的关系。最后,得出结论以及对后续工作的展望。
[Abstract]:The pricing of non - standard American options has been studied by more and more scholars in recent years . The perpetual Bermuda option is a non - standard American option that has no expiry date and can only be selected on a series of time points specified in the contract . The research on the pricing of permanent Bermuda options is not much , and some of the existing research results are highly accurate . Since the perpetual Bermuda option has an optimal execution boundary , the optimal execution boundary of the perpetual American option is often replaced by the optimal execution boundary of the perpetual American option , but no one has ever studied whether the substitution is valid . This paper will solve the optimal execution boundary and pricing of the permanent Bermuda options by using the high - precision configuration method . By the application of the high - precision configuration method , the pricing and the optimal execution strategy of the permanent Bermuda options with higher accuracy are obtained . And the validity of the optimal execution boundary of the permanent American option is verified by comparing with the fixed American option pricing and the optimal execution boundary . This paper first introduces the concept and pricing research review of the permanent Bermuda options , as well as the permanent American option and the high - precision configuration method . Secondly , the optimal execution boundary and the pricing integral expression of the permanent Bermuda options are solved by the high - precision configuration method . Then , the relationship between the perpetual American option and the optimal execution boundary of the perpetual Bermuda option is studied by MATLAB . Finally , the conclusion is drawn and the prospect of the follow - up work is discussed .

【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】：F224;F830.9

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