Mutual Information between Order Book Layers.

The order book is a list of all current buy or sell orders for a given financial security. The rise of electronic stock exchanges introduced a debate about the relevance of the information it encapsulates of the activity of traders. Here, we approach this topic from a theoretical perspective, estimating the amount of mutual information between order book layers, i.e., different buy/sell layers, which are aggregated by buy/sell orders. We show that (i) layers are not independent (in the sense that the mutual information is statistically larger than zero), (ii) the mutual information between layers is small (compared to the joint entropy), and (iii) the mutual information between layers increases when comparing the uppermost layers to the deepest layers analyzed (i.e., further away from the market price). Our findings, and our method for estimating mutual information, are relevant to developing trading strategies that attempt to utilize the information content of the limit order book.

Forecasting Quoted Depth With the Limit Order Book.

Liquidity plays a vital role in the financial markets, affecting a myriad of factors including stock prices, returns, and risk. In the stock market, liquidity is usually measured through the order book, which captures the orders placed by traders to buy and sell stocks at different price points. The introduction of electronic trading systems in recent years made the deeper layers of the order book more accessible to traders and thus of greater interest to researchers. This paper examines the efficacy of leveraging the deeper layers of the order book when forecasting quoted depth-a measure of liquidity-on a per-minute basis. Using Deep Feed Forward Neural Networks, we show that the deeper layers do provide additional information compared to the upper layers alone.

Volume Prediction With Neural Networks.

Changes in intraday trading volume are integral to any algorithmic trading strategy. Accordingly, forecasting the change in trading volume is paramount to better understanding the financial markets. This paper introduces a new method to forecast the log change in trading volume, leveraging the power of Long Short Term Memory (LSTM) networks in conjunction with Support Vector Regression (SVR) and Autoregressive (AR) models. We show that LSTM contributes to a more accurate forecast, particularly when constructed as part of a hybrid model with AR. The algorithm is extended to include data about the time of day, helping the model associate the log change in trading volume with the current hour, which yields the best performance of all trials.