Neural Marked Hawkes Process for Limit Order Book Modeling

Streams of various order types submitted to financial exchanges can be modeled with multivariate Temporal Point Processes (TPPs). The multivariate Hawkes process has been the predominant choice for this purpose. To jointly model various order types with their volumes, the framework is extended to the multivariate Marked Hawkes Process by considering order volumes as marks. Rich empirical evidence suggests that the volume distributions exhibit temporal dependencies and multimodality. However, existing literature employs simple distributions for modeling the volume distributions and assumes that they are independent of the history or only dependent on the latest observation. To address these limitations, we present the Neural Marked Hawkes Process (NMHP), of which the key idea is to condition the mark distributions on the history vector embedded with Neural Hawkes Process architecture. To ensure the flexibility of the mark distributions, we propose and evaluate two promising choices: the univariate Conditional Normalizing Flows and the Mixture Density Network. The utility of NMHP is demonstrated with large-scale real-world limit order book data of three popular futures listed on Korea Exchange. To the best of our knowledge, this is the first work to incorporate complex, history-dependent order volume distributions into the multivariate TPPs of order book dynamics.