Limit order book (LOB) simulators are most useful to practitioners when they combine realistic market dynamics, computationally efficient sampling, controllable scenario generation, and the ability to generalize beyond the instruments seen during training---properties that existing agent-based and deep generative simulators provide only partially. We present \textbf{FlowLOB}, a conditional \textbf{flow}-matching generator of \textbf{LOB} trajectories, trained on multiple Hong Kong Exchange (HKEX) symbols at three sampling frequencies ($0.1$s, $1$s, $10$s) in tick-relative representation that transfers to unseen instruments. Because flow and diffusion models admit a common formulation, we train both with identical data, architecture, and budget, and sample both through the same fixed-step ODE solvers, yielding a controlled comparison of sampling efficiency and fidelity. Flow matching attains its best quality with only $10$ ODE-solver steps, whereas diffusion needs many more function evaluations to approach the same fidelity. At this efficient operating point, FlowLOB improves realism over baselines, two learned and two agent-based models, in most distributional metrics at the two finer sampling frequencies. We evaluate counterfactual controllability with a distributional test that asks whether changing a scenario condition moves the generated statistic toward the corresponding real tail regime; FlowLOB satisfies this criterion in most tested settings. Both realism and control effects transfer zero-shot on a held-out symbol. We additionally conduct ablation studies on the network architecture and the learning rate.
Market microstructure simulation aims to model how liquidity, prices, and order flow evolve in electronic financial markets. Since market data reveal only one realized trajectory, many important questions are inherently counterfactual and require realistic trajectory-level simulation. Existing financial generative models, however, often model order events and market states, such as the LOB, in isolation, overlooking the dynamic interaction between order flow and liquidity in market microstructure. We propose the \textbf{M3} (\underline{M}arket \underline{M}icrostructure \underline{M}odel), a state-event generative foundation model for market microstructure dynamics. \textbf{M3} learns to generate future order-flow trajectories, while accounting for the evolving interaction between order events and limit-order-book liquidity. Trained on large-scale order-level real stock market data, \textbf{M3} exhibits predictable scaling behavior, reproduces key market stylized facts, and enables practical simulation-based applications including forecasting, stress testing, and market-impact analysis. These results suggest a scalable foundation-model paradigm for counterfactual market simulation at the microstructure level.
Evolutionary agent-based markets (ABMs) couple several mechanisms -- who reproduces, how price forms, how biased the agents are, how consensus propagates -- yet these are usually fixed by convention, so it is unclear which mechanism controls which emergent property. In a coevolving, endogenous-price simulator with 120 heterogeneous behavioral agents, we make four mechanisms pluggable and run matched 3x20-seed interventions. We find the levers are largely separable. (1) Selection -> diversity: a Quality-Diversity (QD/MAP-Elites) operator robustly raises strategy-mix entropy over truncation top-k (paired Delta entropy +0.27 to +1.12 bits; sign-test p<0.001; CIs exclude 0) and sustains more strategy cycling (strongest in crisis: Delta=+0.070, p=0.0004). (2) Selection does not improve realism: even a per-agent realism reward that provably steers selection does not raise 5-fact realism (Delta_5=-0.11,-0.08,+0.03; not significant). (3) Microstructure -> realism: enabling reflexive price feedback does raise realism (Delta_5=+0.13,+0.20,+0.20; crisis/bull p<0.05, all CIs positive). (4) Behavior -> fragility: amplifying behavioral bias raises a genomic fragility proxy (Delta=+10.5,+11.1,+14.4; bull p<0.001, all CIs positive) while leaving realism flat. The remaining mechanism -- consensus network topology -- shows no robust effect (honest null). The contribution is a decomposition: in these single-mechanism sweeps the mechanisms behave as approximately distinct control knobs over diversity, realism, and fragility.