A q-spin Potts model of markets: Gain-loss asymmetry in stock indices as an emergent phenomenon

TL;DR

This paper introduces a q-spin Potts model to simulate stock market dynamics, revealing how collective agent behavior can produce a natural gain-loss asymmetry in market indices.

Contribution

It extends traditional Ising models by incorporating multiple states, capturing complex herd behaviors and emergent asymmetries in stock market simulations.

Findings

Self-organized gain-loss asymmetry observed in index time series

Model captures collective dynamics of multiple stock states

Demonstrates emergent phenomena from agent interactions

Abstract

Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell) or three options. However, herding effects of competing stocks and the collective dynamics of a whole market may escape our reach in the simplest models. Here I study a q-spin Potts model version of a simple Ising market model to represent the dynamics of a stock market index in a spin model. As a result, a self-organized gain-loss asymmetry in the time series of an index variable composed of stocks in this market is observed.