Evaluating the Statistical Predictability of Meme Stocks: A Case Study on GameStop Using Geometric Brownian Motion and Alternative Stochastic Models

This research investigates whether meme stock price surges—such as the 2021 GameStop rally—can be statistically predicted using classical financial models like Geometric Brownian Motion (GBM) or whether their movements are fundamentally random and sentiment-driven. By focusing on GameStop (GME) as a case study, the paper examines how speculative retail behavior, social media coordination, and viral momentum challenge traditional assumptions of rational, efficient markets. Through empirical modeling and simulation, the study evaluates GBM’s adequacy in explaining the extreme volatility, tail risks, and distributional anomalies of meme stock behavior.

The author uses Monte Carlo simulations and return distribution analysis to compare modeled price paths with observed data, testing key GBM parameters such as drift and volatility against GameStop’s real-world performance. The results show that GBM systematically underestimates the magnitude and frequency of large price swings, producing thinner tails and smoother volatility than actually observed. Heavy-tailed behavior, volatility clustering, and discontinuous jumps—hallmarks of social-media-driven trading—render the GBM framework inadequate. The study then considers alternative stochastic models, such as time-changed Brownian motion and sentiment-based frameworks, which incorporate stochastic volatility and behavioral feedback loops to better capture real market dynamics.

By bridging mathematical finance with behavioral economics, this paper highlights a core insight: speculative assets influenced by collective online sentiment cannot be effectively modeled by traditional Gaussian or log-normal assumptions. Their dynamics are shaped as much by information virality and moral narratives as by fundamental valuation. The research contributes to emerging literature on retail-driven markets by suggesting that predictive modeling for such assets must integrate psychological, social, and informational variables alongside probabilistic tools. In doing so, it reframes meme stocks not merely as anomalies, but as signals of a paradigm shift in how information, technology, and crowd behavior shape asset pricing in the modern digital era.