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

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  • Francesco Romaggi

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.

Suggested Citation

  • Francesco Romaggi, 2025. "Black-Scholes Model, comparison between Analytical Solution and Numerical Analysis," Papers 2510.27277, arXiv.org.
    • Handle: RePEc:arx:papers:2510.27277
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