Learning to simulate realistic limit order book markets from data as a World Agent
Learning to simulate realistic limit order book markets from data as a World Agent
This paper presents a world model approach for simulating limit order book markets, where a single agent is trained directly from historical data to emulate the entire trader population. Two implementations are proposed: an explicit mixture of parametric distributions and a conditional generative adversarial network (CGAN). The explicit model decomposes the generation process into conditional distributions (e.g., order type, side, depth, quantity) fitted using maximum likelihood, while the CGAN uses a Wasserstein GAN with gradient penalty and unrolled training to implicitly learn the joint distribution of market actions conditioned on market state features. Both models support all main order types (market, limit, cancel, replace), overcoming limitations of prior work that only handled limit orders. Experiments on NASDAQ data for four stocks show that both models produce realistic order flow, volumes, spread, and time to fill, with the CGAN demonstrating better adaptability across different stocks and more accurate spread dynamics. Responsiveness tests with a percentage-of-volume agent reveal that both models exhibit price impact and mean reversion consistent with real markets. The CGAN model, despite being less interpretable, offers greater flexibility and realism, making it a promising tool for trading strategy evaluation and market impact studies.
Highlights
- 1Proposes a world model approach for limit order book simulation that learns directly from historical data without agent calibration.
- 2Extends previous CGAN-based world model to support all main market actions: market orders, limit orders, cancel orders, and replace orders.
- 3Introduces an explicit parametric mixture model as an alternative interpretable world agent.
- 4Improves CGAN training stability and realism by unrolling the model during training to handle synthetic market states.
- 5Demonstrates superior realism and responsiveness compared to prior work across multiple stocks and stylized facts.
Methods
- MConditional Generative Adversarial Network (CGAN) with Wasserstein GAN and gradient penalty (WGAN-GP) for implicit generative modeling.
- MExplicit mixture of parametric distributions: multinomial for order type, logistic regression for side, beta-binomial and negative-binomial for depth and quantity.
- MUnrolled training of CGAN: generating k steps ahead and feeding synthetic states to the critic to improve stability.
- MMarket state representation using volume imbalance, order-sign imbalance, spread, returns, and absolute volumes.
Results
- RBoth world models generate realistic order type distributions and volumes, outperforming prior work that only modeled limit orders.
- RCGAN model closely reproduces real market spread and time to first fill, while explicit model slightly overestimates volumes and spread.
- RCGAN adapts better to different stocks (AVXL, CNR, AINV, AMZN) than the explicit model, which fails for AMZN depth distribution.
- RBoth models exhibit realistic price impact and mean reversion in response to a POV agent, with CGAN showing stronger mean reversion.
- RGenerated mid-price time-series show diversity and realism comparable to historical data.
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