若干类新型期权定价模型的数值解研究

发布时间：2018-07-27 17:04

【摘要】：金融衍生工具已经发展成为当今国际金融界的主要组成部分，期权-金融衍生工具的重心，现在已经成为理论界们研究的重点和难点，其中怎样对期权进行定价以及如何得到期权定价模型的解是两个必须解决的问题.为了达到金融市场以及不同投资者的各种特殊需求，同时为了防范自己可能面临的各种风险，人们设计创造出了各种有不同特征的变异期权，亚式期权和回望期权是其中的两种，因为它们都具有路径依赖的特征，使得这两种期权比标准期权定价更复杂；CEV模型可以说是几何布朗运动的推广；在多种条件的限制下，，会使得模型满足的方程变得复杂难解，甚至无法给出方程的解析解，而对其数值解进行研究.本文主要利用有限差分法研究了CEV模型下有交易费用且标的资产在BP共同作用下的几何亚式期权定价模型的数值解问题和CEV下有交易费用且标的资产在BP共同作用下的回望期权定价模型数值解的问题.主要做了以下工作：第一章简要介绍了期权定价理论及发展；第二章介绍了本文研究问题的背景及研究方法；第三章首先分别介绍了CEV模型下有交易费用且标的资产在BP共同作用下的几何亚式期权定价模型：以及CEV下有交易费用且标的资产在BP共同作用下的回望期权定价模型：并应用有限差分法给出了模型的数值解法；最后给出了它们的实例分析，验证了解法的有效性.
[Abstract]:Financial derivatives have become the main part of the international financial circle. The focus of the option financial derivatives has become the focus and difficulty of the theoretical circles. How to price the options and how to get the solution of the option pricing model are two problems to be solved. In order to reach the financial market As well as the special needs of different investors, and in order to prevent the various risks that they may face, people have designed and created a variety of different characteristics of variant options, subtype options and return options are two of them, because they all have the characteristics of path dependence, making the two options more complex than the standard option pricing; CEV model can be said to be the extension of geometric Brown movement. Under the restrictions of a variety of conditions, the equation that the model satisfies is difficult to solve, even can not give the analytical solution of the equation, and the numerical solution is studied. This paper mainly uses the finite difference method to study the transaction cost under the CEV model and the common action of the standard assets in the BP. The numerical solution of the underlying geometric Asian option pricing model and the problem of the value solution of the return option pricing model under the joint action of BP under CEV under the joint action of the underlying asset under the action of the transaction cost.
The first chapter briefly introduces the theory and development of option pricing.
The second chapter introduces the background and research methods of this paper.
The third chapter first introduces the geometric Asian option pricing model under the CEV model with transaction costs and the underlying assets under BP.
And the option pricing model with the transaction cost under CEV and the underlying assets under the joint action of BP:
The finite difference method is used to give the numerical solution of the model. Finally, an example is given to demonstrate the effectiveness of the method.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

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