Simulations of financial markets in a Potts-like model

TL;DR

This paper introduces a three-state Potts-like model to simulate financial markets, capturing key stylized facts such as fat-tailed return distributions and long-range correlations, with behavior varying by inactivity rate.

Contribution

It extends previous two-state models by incorporating an inactive state, providing a more comprehensive simulation of market dynamics and stylized facts.

Findings

At low inactivity, the model aligns with the two-state Bornholdt model.

Increased inactivity leads to exponential return distributions.

The model reproduces key stylized facts of financial markets.

Abstract

A three-state model based on the Potts model is proposed to simulate financial markets. The three states are assigned to "buy", "sell" and "inactive" states. The model shows the main stylized facts observed in the financial market: fat-tailed distributions of returns and long time correlations in the absolute returns. At low inactivity rate, the model effectively reduces to the two-state model of Bornholdt and shows similar results to the Bornholdt model. As the inactivity increases, we observe the exponential distributions of returns.