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Entropy of Graphs in Financial Markets

Chun-Xiao Nie () and Fu-Tie Song ()
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Chun-Xiao Nie: Zhejiang Gongshang University
Fu-Tie Song: East China University of Science and Technology

Computational Economics, 2021, vol. 57, issue 4, No 8, 1149-1166

Abstract: Abstract This article analyzes the eigenvalues of financial graphs and discusses different types of graphs using random graph theory. We found that the energy-based Rényi index is an effective tool for studying the spectrum of financial graphs. The entropy of financial graphs is usually different from the theoretical predictions of random graph theory, which implies the existence of rich structures. This article also constructed some benchmark graphs for comparative analysis through the classic financial models. The calculations show that the geometric Brownian motion and the one factor model correspond to completely different entropy values based on eigenvalues, thus providing two extreme cases for characterizing real graph entropy. In particular, we find a high correlation between the degree-based Rényi index and the eigenvalue-based Rényi index based on real market data. This article shows the analysis of the structure and complexity of financial graphs from the perspective of graph entropy, thus providing a new way to analyze different types of financial graphs.

Keywords: Rényi index; Financial graph; Correlation matrix; Eigenvalues (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10614-020-10007-3

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