Modeling Financial Sentiment with a Three-State Lattice Gas: From Agent Interaction to Market-Level Shock Responses

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.

کلیدواژه ها:

Agent-based modeling ، financial markets ، statistical mechanics ، Lattice Gas ، Sentiment Dynamics ، Ising model ، Voter model ، polarization ، Entropy ، Social Media Analysis