标题： Black-Scholes模型，解析解与数值分析的比较 显示英文标题

标题： Black-Scholes Model, comparison between Analytical Solution and Numerical Analysis

摘要： 本文的主要目的是提供对第一个广泛使用的期权定价模型——Black-Scholes模型的总体概述和理解。 历史和背景被呈现出来，并说明其在经济学领域中的实用性和影响。 简要回顾了基本微积分概念，以推导和解决该模型。 然后使用解析方法（变量分离）和数值方法（有限差分法）来求解该方程。 得出结论，以便了解Black-Scholes模型如今是如何被使用的。 最后，附录（A）中编写了一些经济学概念，以帮助读者理解本文；此外，还提供了第二个附录（B），其中包含一些代码脚本，以便读者能够将一些概念付诸实践。 显示英文摘要

摘要： The main purpose of this article is to give a general overview and understanding of the first widely used option-pricing model, the Black-Scholes model. The history and context are presented, with the usefulness and implications in the economics world. A brief review of fundamental calculus concepts is introduced to derive and solve the model. The equation is then resolved using both an analytical (variable separation) and a numerical method (finite differences). Conclusions are drawn in order to understand how Black-Scholes is employed nowadays. At the end a handy appendix (A) is written with some economics notions to ease the reader's comprehension of the paper; furthermore a second appendix (B) is given with some code scripts, to allow the reader to put in practice some concepts.