双指数跳跃扩散模型下的几种期权定价

发布时间：2018-02-15 05:26

本文关键词： 期权定价双指数跳跃扩散双障碍期权拉普拉斯变换　出处：《山东大学》2013年硕士论文　论文类型：学位论文

【摘要】：作为一种非常重要的金融衍生产品,期权从一出现就成为金融领域的研究热点,期权定价理论成为现代金融学理论的核心内容之一,吸引了无数专家学者的注意。1973年,Fischer Black和Myron Scholcs提出了著名的Black-Scholcs期权定价模型[1],成为了金融衍生产品定价领域的基石。然而Black-Scholes模型是建立在非常理想的市场假设之下的,与现实情况不符,实际情况下市场存在的不确定因素有很多,因此许多学者在此模型的基础上从不同角度对它进行了推广。从实证的角度考察,Black-Scholcs模型有两个缺陷,一个是波动率微笑,另一个是非对称的尖峰厚尾现象。为了解释这两个现象很多学者提出了不同的模型。其中S.G.Kou于2002年提出了双指数跳跃扩散模型(DEJ)[2],对以上两个实际中出现的现象做出了合理的解释,此外该模型除了能给出普通期权的解析表达式,还能给出一些奇异期权,比如障碍期权(barrier option)、回溯期权(lookback option)的解析定价公式。本文介绍了经典的Black-Scholcs模型,给出了标的资产服从双指数跳扩散的欧式看涨期权的定价。之后介绍了双指数跳跃扩散模型下的障碍期权定价。然后我们用一种新的方法,利用拉普拉斯变换给出了双指数跳跃扩散模型下的双障碍期权的解析定价公式。文章最后探讨了欧式看涨期权定价模型参数的敏感性,对国内市场上存在的一只权证进行的研究,得出了比经典的Black-Scholcs模型更好结果。
[Abstract]:As a very important financial derivative product, option has become a hot research topic in the field of finance since it appeared. Option pricing theory has become one of the core contents of modern finance theory. In 1973, Fischer Black and Myron Scholcs put forward the famous Black-Scholcs option pricing model [1], which became the cornerstone of the field of financial derivatives pricing. However, the Black-Scholes model is based on very ideal market assumptions. Contrary to the reality, there are many uncertain factors in the market, so many scholars generalize it from different angles on the basis of this model. There are two defects in Black-Scholcs model from the empirical point of view. One is the volatility smile, In order to explain these two phenomena, many scholars put forward different models. In 2002, S.G. Kou put forward a double exponential jump diffusion model (DEJ) [2]. There is a reasonable explanation. In addition, the model can not only give the analytic expressions of ordinary options, but also give some analytic pricing formulas for some strange options, such as barrier options, backtracking options, and lookback options. In this paper, the classical Black-Scholcs model is introduced, and the pricing of European call options with the diffusion of underlying assets from the double exponential jump is given. Then, the pricing of barrier options under the double exponential jump diffusion model is introduced. Then we use a new method. By using Laplace transform, the analytical pricing formula of double barrier options under the double exponential jump diffusion model is given. Finally, the sensitivity of the parameters of the European call option pricing model is discussed. The research on a warrant in the domestic market shows a better result than the classical Black-Scholcs model.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.91

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