本文主要研究欧式期权和美式期权的定价模型及其比较。首先介绍了欧式期权和美式期权的概念和特点，以及期权定价的基本原理和方法。然后分别介绍了Black-Scholes模型和二叉树方法这两种主要的期权定价模型，包括其产生背景、内容、公式和局限性，并给出了相应的算例。最后对欧式期权和美式期权的定价方法和数学模型进行了比较。本研究可以为期权投资和风险管理提供一定的参考和借鉴，同时也有助于进一步推动期权定价理论和方法的研究和发展。

This paper mainly focuses on the pricing models and comparison of European and American options. Firstly, it introduces the concepts and features of European and American options, as well as the basic principles and methods of option pricing. Then, it separately presents the two main option pricing models, Black-Scholes model and binomial tree methods, including their backgrounds, contents, formulas, and limitations, and provides corresponding examples. Finally, the paper compares the pricing methods and mathematical models of European and American options, analyzes their differences in scope of application, market application, and risk management, and discusses the future directions and prospects of option pricing research. This study can provide some reference and guidance for option investment and risk management, and also contribute to the further research and development of option pricing theory and methods.