SS2P2: A STABLE STATE-SPACE POINT PROCESS FOR LIMIT-ORDER-BOOK SIMULATION

The limit order book simulation and prediction are important for financial market analysis and market making strategies. The existing State-Space Point Process (S2P2) model predicts the next LOB event accurately but suffers from instability when rolled out which leads to drift or explosion in the simulation. We decouple the output heads of the S2P2 model to create a Stable State-Space Point Process (SS2P2) model. The new model incorporates a softmin-bounded rate head and a soft-max mark head, ensuring stability and non-explosiveness in the point-process sense. Decoupling the heads gives us a hard closed-form intensity ceiling that bounds the event count and prevents explosion, while the soft-max mark head keeps the rate neutral at a fixed state so simulation stays stable. On Coinbase BTC, ETH, and SOL order flow against six baselines and three seeds each, we attain the best NLL and type accuracy on two of three assets (SOL NLL 0.27 vs. 0.38) and tie NHP on the third. We pass verified rate calibration on all nine checkpoints where the uncapped S2P2 fails on six, and lead five of twelve stylized facts in closed-loop roll-outs. The SS2P2 model provides a reliable and accurate framework for simulating limit order book events, making it a practical foundation for market-making world models and agent training.