LOB-Impact Benchmark: Emergent Market Impact in Generative Limit Order Book Models

LOB-Impact Benchmark. Emergent Market Impact in Generative Limit Order Book Models. By George Nigmatulin and eight others, from the University of Oxford and UCLA. Published on the nineteenth of October.

Generative models of the limit order book, or LOB, are meant to serve as world models for trading agents. For that to work, they need realistic market impact: the way prices respond when someone trades. If a simulator gets that mechanism wrong, agents learn policies that are optimal inside the simulator but wrong in the real market. Yet existing metrics judge generated streams only by comparing their distributions with historical data. How a model responds counterfactually to an agent's own orders has gone largely unexamined. A stream can look statistically like the past and still react wrongly when a trader starts pushing on it, and a distributional check would never see the difference.

The authors set out to measure exactly that response, and their headline claim is that market impact emerges naturally in neural LOB generators trained only for next-token prediction. To test it, they inject execution-style metaorders into the generated message flow of five autoregressive models across five NASDAQ stocks. The response is measured with estimators taken from the empirical impact literature, and those estimators are first validated on baselines whose physics is known in advance. That validation step matters for trust: if the estimators recover the right answer where the answer is already known, their readings on the neural generators carry more weight.

The benchmark can evaluate any message-level generator, and it runs in three phases. First comes free generation, which reads how persistent the order flow is against how diffusive the price is. Second is metaorder injection, which yields the exponent and the amplitude of the impact law. Third is a window after execution ends, which measures relaxation. Together the three phases follow a trade from before it starts, through its execution, to what happens once it is done.

One further control separates learning from plumbing. Each visible injection is compared with a blind control that exists only in the simulator. That isolates the model's learned response from the standard mechanics of the order book. For every model on every stock, impact is then measured as a function of cumulative metaorder participation. Without the blind control, a price move might simply reflect the order hitting the book, not anything the model had learned about how markets react.

Impact does emerge in these generative models of market data. The measured exponents range from zero point six three to one point two one, slightly above the traditional zero point five of the square-root law of impact. The models tested do not, so far, show impact decaying during the relaxation window. The authors tentatively attribute this to the context windows of the models, which are still short. It is offered as a likely explanation, not a settled one.

Two results sit side by side here. A model trained only to predict the next message already reacts to trading pressure in a way that resembles real markets, while the fading of that pressure afterward is still missing. The benchmark is released as open source so that future generative models for market data can be checked against both.