Limit Order Book Event Stream Prediction with Diffusion Model

Limit order book (LOB) is a dynamic, event-driven system that records real-time market demand and supply for a financial asset in a stream of data. Event stream prediction in LOB refers to forecasting both the timing and the type of events. The challenge lies in modeling the time-event distribution to capture the interdependence between time and event type, which has traditionally relied on stochastic point processes. However, modeling complex market dynamics using stochastic processes, such as Hawkes-based stochastic models, could be overly simplistic, as they rely on predefined or learned kernel functions to model event dependencies, which limits their ability to capture the nonlinear and dynamically evolving nature of financial markets. In this study, we present LOBDIF (LOB event stream prediction with diffusion model), which offers a new paradigm for event stream prediction within the LOB system. LOBDIF learns the complex time-event distribution by leveraging a diffusion model, which decomposes the time-event distribution into sequential steps, with each step represented by a Gaussian distribution. Additionally, we propose a denoising network and a skip-step sampling strategy. The former facilitates effective learning of time-event interdependence, while the latter accelerates the sampling process during inference. By introducing a diffusion model, our approach breaks away from traditional modeling paradigms, offering novel insights and providing an effective and efficient solution for learning the time-event distribution in order streams within the LOB system. Extensive experiments using real-world data from the limit order books of three widely traded assets confirm that LOBDIF significantly outperforms current state-of-the-art methods.