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Mutual Information between Order Book Layers.

Daniel Libman1, Gil Ariel1, Mary Schaps1

  • 1Department of Mathematics, Bar-Ilan University, Ramat Gan 5290002, Israel.

Entropy (Basel, Switzerland)
|March 25, 2022
PubMed
Summary
This summary is machine-generated.

This study quantifies information in financial order books. We found order book layers are related but contain limited mutual information, with deeper layers showing more correlation.

Keywords:
deep layers of order bookentropyentropy estimationlimit order bookmutual informationmutual information estimationprice and volumerecursive copula

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Area of Science:

  • Quantitative Finance
  • Market Microstructure
  • Information Theory

Background:

  • The relevance of order book data in electronic trading is debated.
  • Limit order books aggregate trader activity through buy/sell orders.

Purpose of the Study:

  • To theoretically assess the information content within different layers of the limit order book.
  • To quantify the mutual information between aggregated buy/sell order book layers.

Main Methods:

  • Theoretical analysis of financial order book data.
  • Estimation of mutual information between discrete order book layers.
  • Comparison of mutual information across different depths of the order book.

Main Results:

  • Order book layers are not statistically independent, indicating some information overlap.
  • The mutual information between layers is relatively small compared to the total joint entropy.
  • Mutual information increases from the top layers towards deeper layers of the order book.

Conclusions:

  • Order book layers possess a degree of interdependence, though the information shared is limited.
  • The findings suggest a potential for utilizing order book information in algorithmic trading strategies.
  • The developed method for mutual information estimation is applicable to financial market analysis.