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Equation-based model for the stock market.

Paloma O C Xavier1, A P F Atman2, A R Bosco de Magalhães3

  • 1Programa de Pós-Graduação em Modelagem Matemática e Computacional, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas 7675, Nova Gameleira, Belo Horizonte, MG, CEP 30510, Brazil.

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Summary
This summary is machine-generated.

This stock market model reveals imitation behavior causes instability, resource limits ensure stability, and fair price sensitivity creates oscillations. Stochasticity introduces long-range correlations and heavy-tailed returns.

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Area of Science:

  • Quantitative Finance
  • Agent-Based Modeling
  • Economic Complexity

Background:

  • Understanding stock market dynamics is crucial for financial stability.
  • Existing models often simplify agent behavior and market interactions.
  • The influence of social networks and fundamental analysis on price requires further investigation.

Purpose of the Study:

  • To develop and analyze a novel stock market model.
  • To investigate the impact of agent behavior, trust networks, and fundamental analysis on market dynamics.
  • To explore the origins of price oscillations and return distributions.

Main Methods:

  • Utilizing difference and differential equations to model stock market variables (demand, supply, price).
  • Analyzing a deterministic version of the model to understand the relationship between behavioral drivers and price.
  • Incorporating stochasticity from microeconomic and macroeconomic sources to examine price series properties.

Main Results:

  • Imitation behavior in agents leads to market instability.
  • Finitude of resources is linked to stock index stability.
  • High sensitivity to fair price triggers price oscillations.
  • Stochastic versions of the model exhibit long-range correlations and heavy-tailed return distributions.

Conclusions:

  • Agent-based modeling, incorporating social networks and fundamental analysis, provides insights into market behavior.
  • The model successfully replicates stylized facts of financial markets, such as price oscillations and non-normal return distributions.
  • Further research can extend this model to explore policy interventions and market regulation.