Research program · Learned dynamics & control
Market simulation research
World models of markets: learned simulations of how prices and order books evolve, built with the structure of numerical physics and held to one test. When a model generates a day of trading, does that day measure like a real one?
The question
Can a learned model reproduce a market well enough to stand in for it?
Well enough that the days it generates match real days on the measurements practitioners care about: the cost of trading, how prices respond to order flow and how that response fades, and how behavior shifts between regimes. And if it can, does anything learned inside it survive real trading costs?
Why a model, not an average
Market behavior depends on the market's state. An average measured over all days is wrong on any particular day. Only a model that tracks the current state gives the value that holds now.
Why a simulator
A market that can be simulated faithfully is a place where trading decisions can be learned and stress-tested before they meet real capital.
Why it is hard
A model can predict the next moment well and still generate markets that drift into nonsense. Getting one step right is not the same as getting a day right.
Two views of a market
From price history to every update of the order book.
The same research runs at two depths: the aggregated history that most of the industry studies, and the full order book, where most of the information lives.
Price history at any resolution
Inputs designed to mean the same thing at any timeframe, so that one model can be trained and run from seconds to days without being rebuilt.
The order book in its own time
Every update of the book, read in event time and described in scale-free terms: the cost of trading, the balance of the queues, the depth and shape of the book, and the flow of orders.
One model across instruments
Because every quantity is scale-free, a single model can span instruments whose prices differ by orders of magnitude.
Markets with a known truth
Synthetic markets generated with known parameters, used to prove that the tooling recovers what was put in before it is trusted on real data.
The model
Built like numerical physics, trained like a decision-maker.
Dynamics with physical structure
The model's internal state evolves in continuous time as a driven, dissipative system: order flow pushes it, friction dampens it, and it stays bounded by construction rather than by clipping.
Verified like an integrator
Its numerical order of accuracy is measured, its energy balance is tested, and the timescales read out of it are checked against its own step-by-step behavior.
Regimes kept distinct
The model represents distinct market regimes as distinct states, rather than blurring them into an average that describes no actual day.
Learning inside the model
Decision policies are trained on futures the model imagines, with fees, risk and holding costs in their objective, then paid what real held-out data returned, through the same execution and cost logic.
Judged like a simulator
A model passes only if the markets it generates reproduce measured properties of real markets. Forecast error alone decides nothing.
Negative results kept
Every answer is recorded with its evidence, including the ones that say no. A premise is tested directly before anything is built on it.
How models are judged
The real market has to pass first.
Before the test is allowed to judge a model, it is run on real held-out days as a control. If it cannot accept the real market, its verdict on a model does not count.
The cost of trading
Whether the generated market prices liquidity the way the real one does, at every point in its day.
How prices respond to flow
How price moves in response to orders, and how that response fades with time, measured on the generated days exactly as on the real ones.
How behavior shifts
Whether the market moves between regimes as the real one does, rather than settling into an average.
Stability over a day
Whether the generated market stays realistic when rolled forward for hours, instead of drifting away from anything a real market does.
Prediction is not simulation
The model with the best one-step forecasts can generate the least realistic markets. Judging a simulator by its forecast error picks the wrong model.
The control comes first
The measurement must accept the real market on held-out days before its verdict on any model counts.
Validation discipline
A result that does not survive these is not a result.
Walk-forward with an embargo
Every model is trained on the past and tested on a later period it never saw, with a gap between them so that nothing leaks across.
Paid what reality paid
Policies are scored on what real held-out data actually returned, through the same execution and cost logic used in training.
Corrected for trying
Purged cross-validation and performance statistics corrected for the number of configurations tried, so that the best of many attempts is not mistaken for skill.
Latency and stress
Execution delay is modeled, inputs are stress-tested, and probes check which inputs a decision actually depends on.
Capabilities
The research stack.
Data & corpora
Historical trades and order books assembled into research corpora, with every feature defined by an explicit contract.
Models
World models at the level of price bars and at the level of the order book, and decision policies trained inside them.
Training
Walk-forward splits with an embargo, curricula for training, and supervised experiment runs that record every configuration.
Evaluation
Realized walk-forward evaluation, significance testing with multiple-testing control, latency modeling, stress tests and sensitivity probes.
Synthetic markets
Simulated markets with known ground truth, used to prove that the tooling recovers what was put in before it is trusted on real data.
Research studies
Studies on historical market data, each answering one question with the evidence attached, whether the answer is yes or no.
Connections
The same ideas, elsewhere in our work.
Ultrafast electron dynamics
Both model a driven system evolving in continuous time and steer it through a simulation that can be differentiated: a market pushed by order flow, a molecule pushed by a laser. The numerical care is the same in both.
Trading & research platform
A policy learned in a simulated market only matters once it is executed. The platform is where backtest, paper and live are held to agree, under the same costs the simulation charges.
Robotics & learning lab
Learning a decision-maker inside a model of the world, then confronting it with the real one, is the problem every robot faces between simulation and hardware.
League operations platform
Hidden strength read through noisy results, and hidden state read through order flow: one estimation problem in two settings.
Engage
By partnership.
Every engagement begins with a conversation and is scoped before work begins. Research. Nothing on this page is offered as a tradeable strategy or as advice.
Research partnerships
Joint work with groups that bring data, compute or a problem that needs a faithful simulator.
Subject: PartnershipResearch engagements
A question about a market or a model, answered with reproducible measurement.
Subject: ResearchAccess
Follow the research under confidentiality.
Subject: AccessInvestment
Briefings and a demonstration, under confidentiality.
Subject: Fundingcontact@carbonyl.org