Paper: arXiv 2502.07071

Abstract

Financial markets are complex systems characterized by high statistical noise, nonlinearity, volatility, and constant evolution. Thus, modeling them is extremely hard. Here, we address the task of generating realistic and responsive Limit Order Book (LOB) market simulations, which are fundamental for calibrating and testing trading strategies, performing market impact experiments, and generating synthetic market data. We propose a novel TRAnsformer-based Denoising Diffusion Probabilistic Engine for LOB Simulations (TRADES). TRADES generates realistic order flows as time series conditioned on the state of the market, leveraging a transformer-based architecture that captures the temporal and spatial characteristics of high-frequency market data. There is a notable absence of quantitative metrics for evaluating generative market simulation models in the literature. To tackle this problem, we adapt the predictive score, a metric measured as an MAE, to market data by training a stock price predictive model on synthetic data and testing it on real data. We compare TRADES with previous works on two stocks, reporting a 3.27 and 3.48 improvement over SoTA according to the predictive score, demonstrating that we generate useful synthetic market data for financial downstream tasks. Furthermore, we assess TRADES’s market simulation realism and responsiveness, showing that it effectively learns the conditional data distribution and successfully reacts to an experimental agent, giving sprout to possible calibrations and evaluations of trading strategies and market impact experiments. To perform the experiments, we developed DeepMarket, the first open-source Python framework for LOB market simulation with deep learning. In our repository, we include a synthetic LOB dataset composed of TRADES’s generated simulations.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced deep learning architectures (diffusion models and transformers) and formal statistical metrics (predictive score based on MAE), requiring sophisticated mathematical foundations. It demonstrates high empirical rigor by releasing an open-source framework (DeepMarket), a synthetic dataset, and quantitative backtesting-style experiments comparing against state-of-the-art methods on real market data.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Generate Realistic &<br>Responsive LOB Simulations"] --> B["Data Input:<br>High-Frequency<br>Real Market Data (LOB)"]
  B --> C["Methodology:<br>TRADES Model<br>Transformer-based Denoising Diffusion Probabilistic Engine"]
  C --> D["Computational Process:<br>Conditional Generation<br>State of Market → Order Flows"]
  D --> E["Evaluation:<br>Adapted Predictive Score<br>(MAE: Synthetic Train → Real Test)"]
  E --> F["Key Findings:<br>3.27 & 3.48 SoTA Improvement<br>High Realism & Responsiveness<br>Released: DeepMarket Framework"]

Cited References (114)

  1. A tutorial on energy-based learning (2006)
  2. Wasserstein generative adversarial networks (2017)
  3. The double auction market institution: A survey (2018)
  4. Transformers in time series: A survey (2022) — link
  5. Appendix for TRADES: Generating Realistic Market Simulations with Diffusion Models (2025) — link
  6. Generative adversarial nets (2014)
  7. Deep generative models: Survey (2018)
  8. Denoising diffusion probabilistic models (2020)
and 106 more
  1. Deep unsupervised learning using nonequilibrium thermodynamics (2015)
  2. Deep AutoRegressive Networks (2014) — link
  3. Wavenet: A generative model for raw audio (2016) — link
  4. Diffusion- TS : Interpretable Diffusion for General Time Series Generation (2024) — link
  5. Nice: Non-linear independent components estimation (2014) — link
  6. Variational Inference with Normalizing Flows (2015) — link
  7. Scalable diffusion models with transformers (2023)
  8. PyTorch: An Imperative Style, High-Performance Deep Learning Library (2019) — link
  9. Handbook of Price Impact Modeling (2023)
  10. Adam: A method for stochastic optimization (2014) — link
  11. Symbolic discovery of optimization algorithms (2023) — link
  12. Csdi: Conditional score-based diffusion models for probabilistic time series imputation (2021)
  13. Modeling temporal data as continuous functions with stochastic process diffusion (2023)
  14. Auto-encoding variational bayes (2013) — link
  15. Simplified State Space Layers for Sequence Modeling (2023) — link
  16. Generating realistic stock market order streams (2020)
  17. Generative time series forecasting with diffusion, denoise, and disentanglement (2022)
  18. Diffusion Models for Time Series Applications: A Survey (2023) — link
  19. Generating realistic neurophysiological time series with denoising diffusion probabilistic models (2023) — link
  20. Modeling Time Series Data with Deep Learning: A Review, Analysis, Evaluation and Future Trend (2020) — link
  21. Agent-based simulation of a financial market (2001) — link
  22. Financial market simulation (2004)
  23. Deep reinforcement learning in agent based financial market simulation (2020)
  24. Optimal execution with nonlinear impact functions and trading-enhanced risk (2003)
  25. A brief review of recent artificial market simulation (agent-based model) studies for financial market regulations and/or rules (2016)
  26. Microscopic simulation of financial markets: from investor behavior to market phenomena (2000)
  27. Generative modeling by estimating gradients of the data distribution (2019)
  28. Limit Order Book Simulation with Generative Adversarial Networks (2023)
  29. Forecasting stock prices from the limit order book using convolutional neural networks (2017)
  30. Using deep learning to detect price change indications in financial markets (2017)
  31. The information content of an open limit-order book (2009)
  32. Deeplob: Deep convolutional neural networks for limit order books (2019)
  33. Benchmark Dataset for Mid-Price Forecasting of Limit Order Book Data with Machine Learning Methods
  34. The Price Impact of Order Book Events (2013) — link
  35. A survey on long short-term memory networks for time series prediction (2021)
  36. Limit Order Book Simulations: A Review — → 2402.17359
  37. Recurrent neural networks: design and applications (1999)
  38. Long short-term memory (1997)
  39. State dependent parallel neural hawkes process for limit order book event stream prediction and simulation (2022)
  40. Trades, Quotes and Prices: Financial Markets Under the Microscope (2018) — link
  41. Attention is all you need (2017)
  42. How markets slowly digest changes in supply and demand (2009)
  43. The price impact of order book events (2014)
  44. Scaling laws for neural language models (2020) — link
  45. On Correlated Stock Market Time Series Generation (2023)
  46. Neural Stochastic Agent-Based Limit Order Book Simulation: A Hybrid Methodology (2023) — link
  47. Diffusion models beat gans on image synthesis (2021)
  48. Market-GAN: Adding Control to Financial Market Data Generation with Semantic Context (2024) — link
  49. A generative model of a limit order book using recurrent neural networks (2023)
  50. Learning to simulate realistic limit order book markets from data as a World Agent (2022)
  51. Experiment Tracking with Weights and Biases (2020) — link
  52. Get real: Realism metrics for robust limit order book market simulations (2020)
  53. Modeling and simulation of a double auction artificial financial market (2005)
  54. Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network — → 2309.00638
  55. Towards realistic market simulations: a generative adversarial networks approach (2021)
  56. LOB-Based Deep Learning Models for Stock Price Trend Prediction: A Benchmark Study (2023) — link
  57. Classifier-free diffusion guidance (2022) — link
  58. A tutorial on principal component analysis (2014) — link
  59. Denoising diffusion implicit models (2020) — link
  60. Visualizing data using t-SNE. (2008)
  61. Score-based generative modeling through stochastic differential equations (2020) — link
  62. Maximum likelihood training of score-based diffusion models (2021)
  63. Universal features of price formation in financial markets: perspectives from deep learning (2021)
  64. Deep learning in finance and banking: A literature review and classification (2020)
  65. Financial time series forecasting with deep learning: A systematic literature review: 2005–2019 (2020)
  66. Deep learning for financial applications: A survey (2020)
  67. How informative is the order book beyond the best levels? Machine learning perspective (2022) — link
  68. Deep learning for limit order books (2019)
  69. Measuring the information content of stock trades (1991)
  70. Order placement strategies in a pure limit order book market (2008)
  71. What pieces of limit order book information do are informative? an empirical analysis of a pure order-driven market (2003)
  72. Market microstructure and stock return predictions (1994)
  73. Stock price forecasting with deep learning: A comparative study (2020)
  74. ABIDES: Towards high-fidelity multi-agent market simulation (2020)
  75. Benchmark dataset for short-term market prediction of limit order book in china markets (2021)
  76. Backtesting (2015)
  77. Reliable fidelity and diversity metrics for generative models (2020)
  78. Deep learning for financial time series forecasting in a-trader system (2017)
  79. A stochastic model for order book dynamics (2010)
  80. Bert: Pre-training of deep bidirectional transformers for language understanding (2018) — link
  81. Simplified state space layers for sequence modeling (2022) — link
  82. Autoregressive denoising diffusion models for multivariate probabilistic time series forecasting (2021)
  83. Smoothness and stability in gans (2020) — link
  84. Tackling the generative learning trilemma with denoising diffusion gans (2021) — link
  85. Regular time-series generation using sgm (2023) — link
  86. Time-series generative adversarial networks (2019)
  87. An agent based model of the E-Mini S&P 500 applied to Flash Crash analysis (2012)
  88. Simulating and analyzing order book data: The queue-reactive model (2015)
  89. Statistical modeling of high-frequency financial data (2011)
  90. Limit order books (2013)
  91. Empirical properties of asset returns: stylized facts and statistical issues (2001)
  92. Statistical properties of stock order books: empirical results and models (2002)
  93. Structured denoising diffusion models in discrete state-spaces (2021)
  94. Elucidating the design space of diffusion-based generative models (2022)
  95. Improved denoising diffusion probabilistic models (2021)
  96. D2c: Diffusion-decoding models for few-shot conditional generation (2021)
  97. Conditional text image generation with diffusion models (2023)
  98. Ar-diffusion: Auto-regressive diffusion model for text generation (2024)
  99. Vidm: Video implicit diffusion models (2023)
  100. Video diffusion models (2022)
  101. Catastrophic forgetting and mode collapse in GANs (2020)
  102. Efficient estimation of word representations in vector space (2013) — link
  103. Distributed representations of words and phrases and their compositionality (2013)
  104. Linguistic regularities in continuous space word representations (2013)
  105. The Power of Depth for Feedforward Neural Networks (2016) — link
  106. High-resolution image synthesis with latent diffusion models (2022)

2 of 114 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.