Solvable stochastic dealer models for financial markets

Area of Science:

• * Quantitative Finance
• * Computational Economics
• * Market Microstructure

Background:

• * Empirical financial market laws, such as the power law of price changes, are well-documented.
• * Existing models often struggle to reproduce these fundamental market behaviors accurately.
• * Understanding the microscopic origins of market dynamics is crucial for developing more realistic models.

Purpose of the Study:

• * To introduce a novel class of solvable stochastic dealer models for financial markets.
• * To demonstrate the ability of these models to capture key empirical market laws.
• * To establish a quantitative link between microscopic market behavior and macroscopic market forces.

Main Methods:

• * Development of stochastic dealer models with adjustable parameters.
• * Incorporation of self-modulation of transaction intervals.
• * Integration of a forecasting tendency based on moving averages of price changes.
• * Analysis of model outputs against empirical market data and theoretical market potential forces.

Main Results:

• * The proposed models successfully reproduce the power law of price change observed in real markets.
• * Even simple models, starting close to Poisson noise, become realistic with the addition of two key effects.
• * A quantitative relationship was identified between the microscopic model dynamics and recently discovered market potential forces.

Conclusions:

• * Solvable stochastic dealer models provide a powerful framework for understanding financial market dynamics.
• * Self-modulation of transaction intervals and price forecasting are critical elements for realistic market simulation.
• * The findings offer a microscopic explanation for macroscopic market potential forces, advancing market price modeling.