Towards Realistic and Interpretable Market Simulations: Factorizing Financial Power Law using Optimal Transport

Abstract: We investigate the mechanisms behind the power-law distribution of stock returns using artificial market simulations. While traditional financial theory assumes Gaussian price fluctuations, empirical studies consistently show that the tails of return distributions follow a power law. Previous research has proposed hypotheses for this phenomenon -- some attributing it to investor behavior, others to institutional demand imbalances. However, these factors have rarely been modeled together to assess their individual and joint contributions. The complexity of real financial markets complicates the isolation of the contribution of a single component using existing data. To address this, we construct artificial markets and conduct controlled experiments using optimal transport (OT) as a quantitative similarity measure. Our proposed framework incrementally introduces behavioral components into the agent models, allowing us to compare each simulation output with empirical data via OT distances. The results highlight that informational effect of prices plays a dominant role in reproducing power-law behavior and that multiple components interact synergistically to amplify this effect.