1973年，Fischer Black与Myron Scholes联合发表了文章《The Pricing of Options and Corporate Liabilities》，给出了日后应用广泛的B-S期权定价公式。 本文将分为四个部分。在第一部分，将介绍一些经济学的基本概念，并分析看涨期权在到期日的价值。在第二部分，经典的二叉树资产定价方法和风险中性定价方法将被证明等价，然后我们将把模型推广到多时段情形。在论文的第三部分，首先由对称随机游动产生并定义布朗运动，并证明二叉树资产定价模型的股价的极限分布服从布朗运动，然后证明布朗运动的伊藤-德布林公式，并利用该公式获得B-S-M方程的解，从而推导出B-S公式。在第四部分，我们将利用2015年开始的上证50ETF期权交易数据，对B-S公式进行检验。

In 1973, Fischer Black and Myron Scholes published an article titled The Pricing of Options and Corporate Liabilities, in which they developed the well-known B-S formula. The thesis is divided into four parts. In the first part, few basic economic concepts will be introduced, and the value of European call options in the mature day will be discussed. In the second part, classical binary tree asset pricing model is proved to be equivalent to risk neutral pricing model, and the model will be expanded to multi-period cases. In the third part, the price of shares will be proved to obey Brownian movement in the limiting cases. After that, we solve the B-S-M equation with Ito-Doeblin formula and the B-S formula is derived. In the last part, we will exam the formula with trading data of Shanghai 50ETF options from 2015 to 2017.