State Dependent Parallel Neural Hawkes Process for Limit Order Book Event Stream Prediction and Simulation

Abstract

The majority of trading in financial markets is executed through a limit order book (LOB). The LOB is an event-based continuouslyupdating system that records contemporaneous demand ('bids' to buy) and supply ('asks' to sell) for a financial asset. Following recent successes in the literature that combine stochastic point processes with neural networks to model event stream patterns, we propose a novel state-dependent parallel neural Hawkes process to predict LOB events and simulate realistic LOB data. The model is characterized by: (1) separate intensity rate modelling for each event type through a parallel structure of continuous time LSTM units; and(2) an event-state interaction mechanism that improves prediction accuracy and enables efficient sampling of the event-state stream. We first demonstrate the superiority of the proposed model over traditional stochastic or deep learning models for predicting event type and time of a real world LOB dataset. Using stochastic point sampling from a well trained model, we then develop a realistic deep learning-based LOB simulator that exhibits multiple stylized facts found in real LOB data. CCS CONCEPTS• Mathematics of computing → Time series analysis; • Computing methodologies → Neural networks; • Applied computing → Economics.

Continuous‐time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

“…Due to the size of the datasets and the high-dimensionality, calibrating simulation models of order book dynamics to data are computationally challenging. Recent examples of such model frameworks for the simulation of the order books include Morariu-Patrichi and Pakkanen (2022), Bellani et al (2021), Shi and Cartlidge (2022), Lu and Abergel (2018), Kumar (2021). Morariu-Patrichi and Pakkanen (2022), Bellani et al (2021), Shi and Cartlidge (2022), Lu andAbergel (2018), andKumar (2021) develop stochastic point process models to model the event-by-event dynamics in order books.…”

“…Neural network (or "neural SDEs") have been widely studied in the financial mathematics literature (Arribas et al, 2020;Cohen et al, 2023Cohen et al, , 2022Cohen et al, , 2022bGierjatowicz et al, 2020;Ni et al, 2021). Neural network Hawkes processes (or "neural Hawkes processes") have also been recently studied and implemented in a number of papers for modeling order book data (Kumar, 2021;Lu and Abergel, 2018;Shi & Cartlidge, 2022). We consider the following neural ).…”

“…where 𝑓, 𝑔, ℎ, 𝜅 are neural networks with collective parameters 𝜃 and where λ𝜃 𝑡 , 𝑁 𝜃 𝑡 , and 𝑆 𝜃 𝑡 can be multidimensional. Recurrent neural networks Hawkes models for order books have been investigated in Kumar (2021) and Shi and Cartlidge (2022). Recurrent neural network Hawkes processes have recently received significant interest in the broader machine learning community (Mei & Eisner, 2017).…”

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