Statistical pairwise interaction model of stock market

TL;DR

This paper demonstrates that a pairwise statistical model based on empirical data effectively captures the complex interactions in stock markets, resembling an Ising model on a network, with implications for understanding market dynamics.

Contribution

It shows that a data-driven pairwise model can accurately represent stock market interactions without restrictive assumptions, linking market structure to spin glass theory.

Findings

Interaction strengths scale inversely with system size

Model captures multiple equilibria and metastable states

Potential to explain market phenomena like order-disorder transitions

Abstract

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or others are agent-based models with rules designed in order to recover some empirical behaviours. Here we show that the pairwise model is actually a statistically consistent model with observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach based only on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviours, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.