Deep Learning for Limit Order Books

TL;DR

This paper introduces a novel spatial neural network architecture tailored for modeling the complex joint distribution of limit order books, leveraging deep information from multiple levels to improve predictive accuracy and risk management applications.

Contribution

The paper presents a new neural network architecture specifically designed for limit order books, enhancing modeling efficiency and accuracy by exploiting spatial structure and deep order book information.

Findings

Outperforms naive empirical, logistic regression, and standard neural network models.

Especially improves tail distribution predictions relevant for risk management.

Effectively models joint distribution of limit order book states.

Abstract

This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient and specifically designed to take advantage of the spatial structure of limit order books. The new architecture yields a low-dimensional model of price movements deep into the limit order book, allowing more effective use of information from deep in the limit order book (i.e., many levels beyond the best bid and best ask). This "spatial neural network" models the joint distribution of the state of the limit order book at a future time conditional on the current state of the limit order book. The spatial neural network outperforms other models such as the naive empirical model, logistic regression (with nonlinear features), and a standard neural network architecture. Both neural networks strongly outperform the logistic regression model. Due to its more effective use of information deep in the limit order book, the spatial neural network especially outperforms the standard neural network in the tail of the distribution, which is important for risk management applications. The models are trained and tested on nearly 500 stocks. Techniques from deep learning such as dropout are employed to improve performance. Due to the significant computational challenges associated with the large amount of data, models are trained with a cluster of 50 GPUs.