摘要：在本文中我给出了一种将正则定价与隐含二叉树定价相结合的美式期权定价方法，并对其进行推导试验。正文中我首先详细的介绍了一些简单的期权定价理论基础，然后我总结了正则法以及二叉树法定价的方法。这对我在后面对正则定价和隐含二叉树定价的结合进行理解，更好的找到正则定价、二叉树定价和美式期权之间的联系，提供有力的论据和探讨的大致方向。之后我介绍了定价过程中的样本处理方法、思路及定价模型的递推公式推导过程。最后通过excle和Matlab进行编程处理，详细描述了定价的操作过程，并对我推导出的定价方法进行实际操作，最后就本方法对数据模拟进行了数值试验和实证分析，得出该方法的可行性结论。71989

本文研究所涉及的理论和方法有风险中性定理、二叉树法、隐含二叉树法和正则定价法等。另外我还使用了 excle 和Matlab来编程。

毕业论文关键词：  二叉树；隐含二叉树；正则分布；美式期权；期权定价；数值试验

American Option Regular Implicit Binary Tree Pricing 

Abstract：In this paper, I will give a formal pricing and implicit binary tree pricing combined with the American option pricing method, and its derivation test。 In the text, I first introduced some simple theoretical basis of option pricing, such as the definition and classification of options, and then I summarize the method of regular and binary tree pricing。 This gives me an understanding of the combination of regular pricing and implied binary tree pricing, better finding the link between regular pricing, binary tree pricing and American options, providing strong arguments and general directions for discussion。 Then I introduced the process of deducing the formula of the sample processing method, the thinking and the pricing model in the pricing process。 Finally, the operation process of pricing is described in detail, and the pricing method is deduced。 Finally, the method is analyzed by numerical experiment, and the feasibility conclusion of the method is obtained。

The theories and methods involved in this paper are risk neutral theorem, binary tree method, implicit binary tree method and regular pricing method。 Also I used the excle and Matlab to program。

Key words：Binary tree；Implicit binary tree；Regular distribution；American options；Option pricing；Numerical test  

目录

摘要 i

Abstract i

目录 ii

1 绪论 1

1。1 研究背景与意义 1

1。2 本文的内容结构 2

1。3 涉及的理论和方法 2

2 期权定价理论概述 3

2。1 期权的定义和分类 3

2。2 期权的定价理论基础 3

2。3 隐含二叉树法 4

2。3。1 经典二叉树模型 4

2。3。2 隐含二叉树法 6

2。4 正则定价 8

2。4。1 正则定价原理 8

2。4。2 正则定价的特点 8

3 美式期权正则隐含二叉树法定价 10

4 程序实现过程描述 13

4。1 主界面的设计 13

4。2 构建定价计算表如图