Deep learning for limit order books

This paper develops a new neural network architecture for modeling spatial distributions (i.e. distributions on $ \mathbb {R}^d $ Rd) which is more computationally efficient than a traditional fully-connected feedforward architecture. The design of the architecture takes advantage of the specific structure of limit order books. The new architecture, which we refer to as a ‘spatial neural network’, 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). The 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 status quo 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 U.S. 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.