Emergence of universal scaling in financial markets from mean-field dynamics

TL;DR

This paper introduces a microscopic mean-field model explaining the universal scaling behaviors observed in financial markets, capturing key empirical properties like price fluctuation distributions and volatility correlations.

Contribution

It presents a novel mean-field framework that links agent interactions via a global variable, accurately reproducing universal scaling phenomena in financial data.

Findings

Reproduces universal scaling of price fluctuations

Captures long-range volatility correlations

Models multiscaling in financial time series

Abstract

Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction dynamics between individual components is mediated by a global variable making the mean-field description exact. Using the example of financial markets, we show that asset price can be such a global variable with the critical role of coordinating the actions of agents who are otherwise independent. The resulting model accurately reproduces empirical properties such as the universal scaling of the price fluctuation and volume distributions, long-range correlations in volatility and multiscaling.