Recreating multifractality in financial markets

What do financial markets, sunspots, and brain dynamics have in common? They all exhibit multifractal behavior — an interwoven repeating pattern spanning multiple scales. Multifractality is common in nature, but not well understood. Models attempting to reflect these systems often fail to replicate multifractal dynamics, making them challenging to study.

Kowalski et al. used an agent-based model to replicate multifractal dynamics in stock market data. Their approach seeks to determine whether multifractality is an emergent phenomenon in systems with simple rules.

“My main question was: What conditions does a system need to produce multifractal behavior?” said author Paweł Oświęcimka. “Are any special conditions needed for the elements of the system to produce such amazing collective behavior? Or does it emerge almost spontaneously as a balance between collective and spontaneous behavior?”

To answer this question, the authors built a multi-agent stock trading model where each simulated agent can make trades independently. These agents take into account both the positions of nearby agents — buying, selling, or inactivity — and the overall market sentiment and decide whether to trade stocks.

Although the system itself has very few rules, the authors found that complex multifractal behavior emerges anyway. They found separate regimes of collective behavior and agent freedom, with the model undergoing something akin to a phase transition when moving between the regimes. At the border of these two regimes, where individual actions are balanced with collective behavior, multifractality emerges.

“The natural next step is to apply [this model] to simulate the dynamics of other complex systems, such as the brain, especially in the context of neurodegenerative disease, since it can help us describe changes in brain dynamics from the perspective of multifractal behavior,” said Oświęcimka.

Source: “Emergent multifractality in a multi-asset three-state agent-based market model,” by Rafał Kowalski, Paweł Oświęcimka, and Stanisław Drożdż, Chaos (2026). The article can be accessed at https://doi.org/10.1063/5.0347841 .