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.
Highlights
Stock exchanges provide an organized platform for traders to exchange securities, which is known as the limit order book
Our results show that as we dive deeper into the limit order book, the mutual information between the layers increases
The results in this contribution show that the amount of mutual information slightly increases as the layer depth increases, suggesting that each successive layer of the limit order book is more similar to the one that preceded it
Summary
A limit order is an agreement to buy (or sell) a given number of shares of a particular stock at a given price (or better). This type of order is usually not fulfilled immediately and is instead listed in the limit order book while waiting for a match. Market orders are orders to buy or sell at the best currently available price in the limit order book. Since these orders have no price restrictions, market orders are typically fulfilled instantaneously
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