Neural stochastic agent‐based limit order book simulation with neural point process and diffusion probabilistic model

Modern financial exchanges use an electronic limit order book (LOB) to store bid and ask orders for a specific financial asset. As the most fine‐grained information depicting the demand and supply of an asset, LOB data are essential in understanding market dynamics. Therefore, realistic LOB simulations offer a valuable methodology for explaining the empirical properties of markets. Mainstream simulation models include agent‐based models (ABMs) and stochastic models (SMs). However, ABMs tend not to be grounded on real historical data, whereas SMs tend not to enable dynamic agent‐interaction. More recently, deep generative approaches have been successfully implemented to tackle these issues, whereas its black‐box essence hampers the explainability and transparency of the system. To overcome these limitations, we propose a novel hybrid neural stochastic agent‐based model (NS‐ABM) for LOB simulation that incorporates a neural stochastic trader in agent‐based simulation, characterised by (1) representing the aggregation of market events' logic by a neural stochastic background trader that is pre‐trained on historical LOB data through a neural point process model; (2) learning the complex distribution for order‐related attributes conditioned on various market indicators through a non‐parametric diffusion probabilistic model; and (3) embedding the background trader in a multi‐agent simulation platform to enable interaction with other strategic trading agents. We instantiate this hybrid NS‐ABM model using the ABIDES platform. We first run the background trader in isolation and show that the simulated LOB can recreate a comprehensive list of stylised facts that demonstrate realistic market behaviour. We then introduce a population of ‘trend’ and ‘value’ trading agents, which interact with the background trader. We show that the stylised facts remain and we demonstrate order flow impact and financial herding behaviours that are in accordance with empirical observations of real markets.