Mutual Information between Order Book Layers

Abstract

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.

The Linear Relationship Model with LASSO for Studying Stock Networks

“…We recently proposed to use mutual information to measure the nonlinear dependencies between stocks [ 21 , 22 ]. The information theory has been used recently to study stock relationship networks and other related financial problems [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. It is important to emphasize that the complexity of stock market systems may lead to a number of interactive patterns among stocks, and hence different measurements are needed to produce financial networks.…”