有交易费用的离散型算术平均亚式期权的近似定价

发布时间：2018-04-17 22:31

本文选题：交易费用 + 离散型　；参考：《华中师范大学》2013年硕士论文

【摘要】：为了满足金融市场发展的需要,二十世纪九十年代,亚式期权作为一种新型期权(路径依赖的期权)首次在日本东京问世。亚式期权有三大优点：(1)能有效防止人为操纵标的资产的价格,维护市场公平性；(2)对于套期保值者而言,产生的金融风险相对较小；(3)相比标准的欧式期权,其自身的价格也比较便宜。因此,亚式期权的优势更加明显,它已逐渐成为市场关注的焦点,其定价问题也成为人们研究的热点。亚式期权主要有两种类型：一是几何平均亚式期权,二是算术平均亚式期权。对于前者而言,其标的资产价格的几何平均值仍满足对数正态分布,因此可用经典的方法为其求解,但对于后者而言,其标的资产价格的算术平均值却不满足对数正态分布,通常采用近似的方法为算术平均亚式期权定价。本文研究算术平均亚式期权的定价问题,并对有交易费用的离散型算术平均亚式期权的定价问题进行了深入探讨,分为到期日较短和较长两种情形。对于到期日较短的情形采用的是蒙特卡洛的数值方法,而对于到期日比较长的情形则采用如下的近似定价方法,即先把期权有效期内某个时间段[t,T]均分成M-1个时间段,并计算这M个时间点上的期望收益,然后求和取平均,比较此平均值与有交易费用的离散型算术平均亚式期权的期望收益之间的渐进关系,得到一个近似解,从而为有交易费用的离散型算术平均亚式期权进行近似定价,最后,本文给出了一个相关的数值例子。
[Abstract]:In order to meet the needs of the development of financial market, Asian option, as a new type of option (path dependent option), was first introduced in Tokyo, Japan in the 1990s.Asian option has three major advantages: 1) it can effectively prevent artificial manipulation of the price of the underlying asset and maintain market fairness. For hedgers, the financial risk generated is relatively small) compared with the standard European option.Its own price is also relatively cheap.Therefore, the advantage of Asian option is more obvious, it has gradually become the focus of market attention, and its pricing has become a hot topic.There are two main types of Asian options: one is geometric average Asian option, the other is arithmetic average Asian option.For the former, the geometric average value of the underlying asset price still satisfies the logarithmic normal distribution, so it can be solved by the classical method, but for the latter, the arithmetic average of the underlying asset price does not satisfy the logarithmic normal distribution.An approximate method is usually used to price the arithmetic average Asian option.In this paper, the pricing problem of arithmetic average Asian option is studied, and the pricing problem of discrete arithmetic average Asian option with transaction costs is discussed in depth, which can be divided into two cases: shorter maturity date and longer maturity date.In the case of shorter maturity date, Monte Carlo numerical method is used, while in the case of long maturity date, the approximate pricing method is used, that is to say, [t T] is divided into M-1 time periods in a certain period of validity of an option.The expected income at M time points is calculated, then the sum is averaged, and the asymptotic relationship between the mean value and the expected return of discrete arithmetic average Asian option with transaction costs is compared, and an approximate solution is obtained.In order to approximate the pricing of discrete arithmetic average Asian options with transaction costs, a numerical example is given in this paper.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

【参考文献】