DigMA: Controllable Generation of Financial Market Data – A Deep Dive

Background

Generative modeling has transformed natural language processing, vision, and scientific discovery, but its application to financial markets remains limited. Order‑flow, the finest‑granular event in markets, is essential for studying micro‑structure and interaction mechanisms, making order‑flow modeling a fundamental generative task.

Existing rule‑based and learning‑based agents suffer from low fidelity and limited flexibility. Rule‑based agents rely on oversimplified assumptions and are not trained on real data, while learning‑based agents often capture only local distributions and ignore long‑range dynamics. Moreover, prior work lacks controllability, which is crucial for scenario‑based experiments and counterfactual analysis.

Problem Definition

The goal is controllable financial‑market generation: given a target scenario described by aggregated statistics (e.g., daily return, daily amplitude, intraday volatility), generate an order‑flow that matches these statistics while preserving high fidelity. Formally, the task is to learn a conditional sampler p_{M}(O\mid a), where O is an order‑flow sample and a is the control target. The objective minimizes the distance between the target metrics and those of the generated flow, and simultaneously minimizes the divergence between the real and generated “stylized‑facts” distributions.

The fidelity term is expressed as the KL divergence between the real and generated stylized‑facts distributions.

Method

DigMA consists of two modules: a meta‑controller c and an order generator G.

3.1 Meta‑Controller

The meta‑controller learns the intra‑day dynamics of latent market states x, represented by intermediate price return r and order‑arrival rate λ. It fits the distribution of these states using a conditional diffusion process that generates latent variables from noise.

Training employs an ϵ‑parameterized denoising diffusion probabilistic model (DDPM) that predicts injected noise. The loss is the mean‑squared error between predicted and true noise.

For controllability, the diffusion model is conditioned on scenario variables via a feature extractor φ that projects the target metrics into a latent representation φ(c). Both discrete and continuous control encoders are designed, and classifier‑free guidance is used during sampling.

During sampling, the guidance score combines unconditional and conditional diffusion scores.

The sampling process iteratively denoises from x_N to x_0.

3.2 Order Generator

The order generator comprises a simulated exchange (implementing a double‑auction protocol) and a meta‑agent that aggregates the behavior of all market participants. For each trading minute t, the meta‑agent draws a waiting time Δ_i from an exponential distribution with rate λ_t (provided by the meta‑controller). Upon “waking”, an actor agent A_i is instantiated.

The actor agent follows four steps:

Initialization: Randomly set holdings S, cash C, and heterogeneous component weights g_f, g_c, g_n for fundamentals, chart analysis, and noise.

Return Estimation: Compute a weighted average of the three components to estimate future return.

Position Optimization: Estimate future price and solve a CARA utility maximization to obtain a demand function.

Order Sampling: Uniformly sample an order price between the minimum acceptable price p_l and the estimated price, then determine order quantity q_i = u(p_i) - S and sign o_i = sign(q_i). Generation stops at t_{max}.

Experiments

4.1 Datasets and Model Configuration

Two tick‑level order‑flow datasets from the Chinese stock market (A‑Main and ChiNext) are used. Each dataset provides 5,000 samples for validation, 5,000 for testing, and the remainder for training. The diffusion model is trained for 10 epochs with 200 diffusion steps, AdamW optimizer, batch size 256, and learning rate 1e‑5. During training, conditional information for discrete and continuous controllers is randomly dropped with probability 0.5.

4.2 Controllable Generation Evaluation

Three metrics—return, amplitude, and volatility—are discretized into five percentile‑based bins to define scenarios. DigMA is trained with both discrete and continuous control encoders. Compared to uncontrolled baselines, DigMA achieves consistently low error across all metrics, demonstrating strong controllability.

4.3 Fidelity Evaluation

DigMA is compared against rule‑based (RFD), learning‑based (RMSC), and GAN‑based (LOBGAN) baselines. Stylized‑facts such as minute log‑returns, return autocorrelation, volatility clustering, and order‑imbalance ratio are examined. DigMA attains the lowest KL divergence on most metrics, indicating superior market‑simulation fidelity.

4.4 High‑Frequency Trading Reinforcement‑Learning Evaluation

DigMA serves as the training environment for an A2C‑based trading agent. Environments include historical replay, RFD, DigMA, and DigMA without the meta‑controller (DigMA‑c). Evaluation metrics are daily return, daily volatility, Sharpe ratio, and maximum drawdown. Agents trained in DigMA achieve the highest daily return and Sharpe ratio, while DigMA‑c yields the lowest volatility and drawdown, confirming DigMA’s effectiveness for strategy learning.

4.5 Computational Efficiency

Generation latency (average time per order) is measured across all baselines. DigMA generates an order in approximately 0.017 ms, the fastest among compared methods, making it suitable for real‑time, latency‑sensitive applications.

Conclusion

DigMA introduces a diffusion‑guided meta‑agent framework that achieves controllable, high‑fidelity generation of financial market order‑flow. Extensive experiments demonstrate its superiority over rule‑based and learning‑based baselines in controllability, fidelity, reinforcement‑learning utility, and computational speed, establishing DigMA as an effective synthetic environment for downstream high‑frequency trading research.