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Modeling Financial Sentiment with a Three-State Lattice Gas: From Agent Interaction to Market-Level Shock Responses | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 2، مهر 2026، صفحه 183-209 اصل مقاله (654.16 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2026.92434.1282 | ||
| نویسندگان | ||
| Halim Zeghdoudi* 1؛ Fatih Tank2 | ||
| 1LaPS Laboratory, Badji Mokhtar-Annaba University, Annaba, Algeria | ||
| 2Department of Economics, Atilim University, Ankara, Turkey | ||
| چکیده | ||
| This paper develops an agent-based framework for studying financial sentiment dynamics through a three-state lattice gas model in which agents hold bullish, neutral, or bearish positions. Extending classical binary models such as the Ising and voter models, the framework introduces a neutral state to capture hesitation, indecision, and temporary withdrawal from directional beliefs, especially during uncertain market conditions. Sentiment changes are driven by local interactions among neighboring agents and external information shocks, with reversible stochastic dynamics governing the updating process. Analytical results and numerical simulations show the emergence of persistent opinion clusters, entropy shifts under information stress, and gradual recovery toward balance after strong shocks. Empirical illustrations using sentiment extracted from financial social-media data suggest that the model can reproduce key patterns in market reactions. Compared with standard binary approaches, the three-state formulation better captures uncertainty, the buffering role of neutral agents, asymmetric shock responses, and recovery dynamics, making it a useful framework for linking individual sentiment updates to collective market behavior. | ||
| کلیدواژهها | ||
| Agent-Based Modeling؛ Financial Markets؛ Statistical Mechanics؛ Lattice Gas؛ Sentiment Dynamics؛ Ising Model؛ Voter model؛ Polarization؛ Entropy؛ Social Media Analysis | ||
| مراجع | ||
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[1] E. Ising, Beitrag zur Theorie des Ferromagnetismus, Zeitschrift für Physik, (1925) 31, 253–258. https://doi.org/10.1007/BF02980577 [2] P. Clifford, and A. Sudbury, A model for spatial conflict, Biometrika, (1973) 60(3), 581–588. https://doi.org/10.1093/biomet/60.3.581 [3] H. Zeghdoudi, and H. Boutabia, Computation for the canonical measures of a colored disordered lattice gas and spectral gap, Journal of Mathematical Physics, (2009) 50, 103304. [4] S. Bornholdt, Expectation bubbles in a spin model of markets: Intermittency from frustration across scales, International Journal of Modern Physics C, (2001) 12(5), 667–674. https://doi.org/10.1142/S0129183101001845 [5] C. Castellano, S. Fortunato, and V. Loreto, Statistical physics of social dynamics, Reviews of Modern Physics, (2009) 81(2), 591–646. https://doi.org/10.1103/RevModPhys.81.591 [6] Y. Xu, and S. B. Cohen, Stock movement prediction from tweets and historical prices. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), (2018) pp. 1970–1979. Association for Computational Linguistics, https://doi.org/10.18653/v1/P18-1183 [7] M. Qezelbash, S. Tajdini, F. Jafari, M. Lotfi Ghahroud, and M. Farajnezhad, An analysis of volatility and herd behavior among investors in the S&P500 stock market index, Bitcoin, and gold markets, Journal of Mathematics and Modeling in Finance, (2023) 3(2), 77–92, https://doi.org/10.22054/jmmf.2024.75516.1103 | ||
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