Black-Scholes Model, comparison between Analytical Solution and Numerical Analysis
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911365301534720 |
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| author | Romaggi, Francesco |
| author_facet | Romaggi, Francesco |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_27277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Black-Scholes Model, comparison between Analytical Solution and Numerical Analysis Romaggi, Francesco Pricing of Securities Computational Engineering, Finance, and Science Computational Finance Risk Management 91G80, 35Q91, 65M06, 65M12, 60H30 G.1.8; G.1.10; I.6.5; J.4 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. |
| title | Black-Scholes Model, comparison between Analytical Solution and Numerical Analysis |
| topic | Pricing of Securities Computational Engineering, Finance, and Science Computational Finance Risk Management 91G80, 35Q91, 65M06, 65M12, 60H30 G.1.8; G.1.10; I.6.5; J.4 |
| url | https://arxiv.org/abs/2510.27277 |