亚式期权定价的比较研究

发布时间：2018-01-13 08:43

本文关键词：亚式期权定价的比较研究　出处：《华中师范大学》2014年硕士论文　论文类型：学位论文

【摘要】：亚式期权,它是由美国一家信托公司(Bankers Trust)在欧式期权的基础上提出的一种创新,首次出现在二十世纪九十年代的日本东京。它作为当今金融市场上交易最活跃、应用最广泛的一种强路径依赖型期权,因其价格便宜、易于风险控制、利于套期保值等方面的优势,深受投资者与管理者的喜爱。自2008年全球风暴以来,风险管理与控制再一次成为世界关注的焦点,人们对亚式期权的关注也随之提升了一个层次,其定价问题也逐渐成为衍生品资产定价研究的热点之一。本文主要研究离散型固定敲定价欧式亚式期权的定价问题,首先概述了期权定价的预备知识,然后分别为离散型几何平均亚式期权和离散型算术平均亚式期权定价。对于离散型几何平均亚式期权,若标的资产价格服从对数正态分布,由于一系列对数正态分布的几何平均值仍为对数正态分布,从而可迅速得出几何平均亚式期权定价公式的解析解；对于离散型算术平均亚式期权,由于算术平均后的资产价格不再服从对数正态分布,不能直接利用Black-Scholes公式,其定价公式也只能近似给出,本文分别用均值关系近似定价、泰勒展开近似定价、Monte Carlo模拟、渐进差异近似定价这四种方法来探讨算术平均亚式期权近似定价公式。最后通过Matlab软件编写程序对上述各种定价方法进行实证分析与比较,进而对各种定价方法做了总结与分析。
[Abstract]:Asian option, which is composed of an American trust company (Bankers Trust) is a kind of innovation is proposed on the base of European option, first appeared in Japan in 1990s in Tokyo. As the most active financial market transactions, a kind of strong path dependent options are the most widely used, because of its cheap price, easy to for risk control, hedging and other advantages, favored by investors and managers alike. Since 2008 the global crisis, risk management and control once again become the focus of the world, people of Asian options concern will upgrade to the next level, the pricing problem has gradually become a hot research topic in asset pricing derivatives.
This paper mainly studies the pricing problem of discrete fixed strike European style Asian option pricing, firstly summarizes the preliminary knowledge of option pricing, and then discrete geometric average Asian options and the discrete arithmetic average Asian option pricing. For the discrete geometric average Asian option, if the price of the underlying asset follows the lognormal distribution due to a series of geometry, the lognormal distribution is the average value of the lognormal distribution, which can be quickly obtained analytic geometric average Asian option pricing formula of the solution; for the discrete arithmetic average Asian options, because the arithmetic average asset prices no longer obeys the lognormal distribution, the Black-Scholes formula can not be applied directly, the only the approximate pricing formula is given in this paper, with the mean relation of approximate valuation, Taylor approximation pricing, Monte Carlo simulation, the difference of the four incremental approximate pricing method The approximate pricing formula of arithmetic average Asian option is discussed. Finally, the above pricing methods are empirically analyzed and compared by Matlab software programming, and the various pricing methods are summarized and analyzed.

【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.9

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