Learning who is in the market from time series: market participant discovery through adversarial calibration of multi-agent simulators

In electronic trading markets often only the price or volume time series, that result from interaction of multiple market participants, are directly observable. In order to test trading strategies before deploying them to real-time trading, multi-agent market environments calibrated so that the time series that result from interaction of simulated agents resemble historical are often used. To ensure adequate testing, one must test trading strategies in a variety of market scenarios – which includes both scenarios that represent ordinary market days as well as stressed markets (most recently observed due to the beginning of COVID pandemic). In this paper, we address the problem of multi-agent simulator parameter calibration to allow simulator capture characteristics of different market regimes. We propose a novel two-step method to train a discriminator that is able to distinguish between"real"and"fake"price and volume time series as a part of GAN with self-attention, and then utilize it within an optimization framework to tune parameters of a simulator model with known agent archetypes to represent a market scenario. We conclude with experimental results that demonstrate effectiveness of our method.

💡 Research Summary

The paper addresses the practical problem of calibrating multi‑agent market simulators when only aggregate price and volume time series are observable. Accurate calibration is essential for testing trading strategies across a spectrum of market regimes, from ordinary days to stress periods such as the early COVID‑19 market shock. Traditional approaches struggle because the mapping from simulator parameters to observable time‑series statistics is highly nonlinear and lacks an explicit loss function.

To overcome this, the authors propose MAS‑GAN, a two‑step framework that leverages an adversarially trained discriminator as an implicit objective for simulator calibration. In the first step, a GAN is trained on real market data consisting of concatenated T‑second mid‑price returns and cumulative T‑second traded volumes. Both generator and discriminator are built from 1‑D convolutional layers augmented with multi‑head self‑attention, enabling the network to capture both local temporal dependencies and global cross‑correlations between price and volume. Training follows the Wasserstein GAN with gradient penalty (WGAN‑GP) paradigm, which stabilizes learning and provides a continuous “realism” score rather than a binary classification. The generator must be capable of producing a diverse set of realistic series; the authors monitor visual diversity, convergence of statistical moments, and the discriminator’s inability to separate generated from real data.

In the second step, the trained discriminator D is repurposed as a quantitative measure of similarity: D outputs a probability that a given series is “real.” For a simulator parameter vector v (e.g., arrival rate λ of value agents and number N of noise agents) and a random seed R, the simulated series S_R(v) is fed to D, yielding D(S_R(v)). The calibration objective becomes maximizing the expected discriminator score over random seeds, i.e., v* = argmax_v E_R