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

Paper: arXiv 2507.09863

Authors: Ryuji Hashimoto, Kiyoshi Izumi

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.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts like optimal transport, power-law exponents, and Hill estimators, while also detailing a controlled simulation pipeline with quantitative metrics like OT distances to compare synthetic data against real market data.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Disentangle factors behind<br>power-law distribution of stock returns"] --> B
  B["Methodology<br>Artificial Market Simulations"] --> C
  
  subgraph C ["Data & Inputs"]
      direction LR
      C1["Empirical Equity Data<br>Power-law tails"]
      C2["Incremental Agent Models<br>Behavioral components"]
      C3["Optimal Transport OT<br>Quantitative similarity measure"]
  end
  
  C --> D
  
  subgraph D ["Computational Process"]
      direction LR
      D1["Controlled Experiments<br>Intro behavioral components"]
      D2["Simulate Market Dynamics<br>Price impact & information flow"]
      D3["Compare with Empirical Data<br>Using OT distance metrics"]
  end
  
  D --> E["Key Findings/Outcomes"]
  
  E --> F["Informational effect of prices<br>dominant in power-law reproduction"]
  E --> G["Multiple components interact<br>synergistically to amplify effect"]
  E --> H["Interpretable framework<br>isolates individual contributions"]
  
  style A fill:#e1f5fe,stroke:#01579b,stroke-width:2px
  style B fill:#fff3e0,stroke:#e65100,stroke-width:2px
  style C fill:#f3e5f5,stroke:#4a148c,stroke-width:2px
  style D fill:#e8f5e8,stroke:#1b5e20,stroke-width:2px
  style E fill:#fff9c4,stroke:#f57f17,stroke-width:2px
  style F fill:#ffebee,stroke:#c62828,stroke-width:1px
  style G fill:#ffebee,stroke:#c62828,stroke-width:1px
  style H fill:#ffebee,stroke:#c62828,stroke-width:1px

Cited References (59)

1. The economy needs agent-based modeling (2009)
2. Agent-based models for financial crises (2017)
3. Complexity theory and financial regulation (2016)
4. High-frequency financial market simulation and flash crash scenarios analysis: An agent-based modelling approach (2024)
5. A study on the reversal mechanism for large stock price declines using artificial markets (2012)
6. How to evaluate trading strategies: Single agent market replay or multiple agent interactive simulation? (2019) — link
7. Market making via reinforcement learning (2018)
8. Multi-agent reinforcement learning in a realistic limit order book market simulation (2021)

1 of 59 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.