Black-Scholes Model, comparison between Analytical Solution and Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2510.27277,
title = {Black-Scholes Model, comparison between Analytical Solution and Numerical Analysis},
author = {Francesco Romaggi},
journal= {arXiv preprint arXiv:2510.27277},
year = {2026}
}