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Modeling asset price processes based on mean-field framework.

Masashi Ieda¹, Masatoshi Shiino

¹Department of Physics, Faculty of Science, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan. mieda@mikan.ap.titech.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 7, 2012

Summary

We developed a new microscopic model for financial asset dynamics using a mean-field approach. This model captures market structure interactions and effectively prices options, even with complex noise.

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Area of Science:

Quantitative Finance
Statistical Mechanics
Financial Modeling

Background:

Traditional financial models often overlook the intricate interactions between assets.
A microscopic approach is needed to better understand market structure dynamics.
Existing models may not fully capture complex noise patterns in financial data.

Purpose of the Study:

To introduce a novel mean-field model for financial asset dynamics.
To incorporate inter-asset interactions reflecting market structure.
To demonstrate the model's utility in pricing financial derivatives.

Main Methods:

Application of the mean-field theoretical framework.
Development of a microscopic model for financial markets.
Case study involving European call option pricing.

Main Results:

The proposed model successfully integrates asset interactions.
The mean-field approach provides a robust framework for financial dynamics.
The model demonstrates effectiveness in pricing European call options with short-time memory noise.

Conclusions:

The mean-field model offers a powerful microscopic perspective on financial markets.
This approach enhances the understanding of market structure and asset interactions.
The model shows promise for pricing complex financial derivatives accurately.