A Non-Adversarial World Agent for Limit Order Book Simulation: Training a Conditional Limit Order Book Generator with Signature Kernel Scores

Realistic limit order book (LOB) simulators serve two needs: expanding the limited supply of historical market data with synthetic order streams, and providing reactive environments in which to train and evaluate trading strategies. Traditional agent-based simulators construct a market from many hand-specified traders, but are difficult to calibrate because public data carries no per-participant attribution. The world-model approach instead trains a single ''world agent'' to reproduce the aggregate behavior of the whole market directly from historical data; a leading instantiation is a conditional GAN whose generator, given the recent market state, emits the next order, trained adversarially as a Wasserstein GAN with gradient penalty. We build on this world agent to introduce a new training approach for LOB simulators: we retain the conditional generator but train it against a fixed signature kernel score instead of a learned adversarial critic, turning an unstable adversarial game into a single-network minimization with no critic, no gradient penalty, and no auxiliary losses, and a loss whose value is a fixed objective directly tied to signature kernel MMD. The two strategies do not admit the same training recipe: the non-adversarial objective trains under one fixed configuration across every experiment we report, with no per-run tuning, whereas the adversarial arm needed a shorter training window and three auxiliary stabilization losses to yield a usable checkpoint at all. Under these respective configurations, the non-adversarial model more closely reproduces several order-flow, price-path, volume, and return-tail statistics and avoids the degenerate rollouts observed from the adversarial arm, whereas spread and order size dispersion remain a challenge. The proposed non-adversarial model generalizes across intraday windows and, without retraining, to a security held out entirely from training.