In these days of big data, machine learning, and AI, many researchers are showing growing interest in sophisticated models for stock price prediction or to refine basic models of stock dynamics.
I have written an article that provides a detailed and intuitive explanation of stock price dynamics under geometric Brownian motion, without using stochastic calculus.
The derivation starts from discrete returns and compounding, uses probability and aggregation arguments to explain the emergence of lognormal prices, and shows why the σ²/2 correction arises from Jensen’s inequality rather than from formal calculus.
I have not found this line of explanation in standard texts, and I believe it offers both conceptual clarity and practical insight for anyone applying GBM-based models in trading, pricing, or risk analysis.
https://substack.com/@themarketjourney/p-188597973
I have written an article that provides a detailed and intuitive explanation of stock price dynamics under geometric Brownian motion, without using stochastic calculus.
The derivation starts from discrete returns and compounding, uses probability and aggregation arguments to explain the emergence of lognormal prices, and shows why the σ²/2 correction arises from Jensen’s inequality rather than from formal calculus.
I have not found this line of explanation in standard texts, and I believe it offers both conceptual clarity and practical insight for anyone applying GBM-based models in trading, pricing, or risk analysis.
Thanks for the article. More intuitive than using the SDE.