Structural Entropy: Monitoring Correlation-Based Networks Over Time With Application To Financial Markets

Abstract

The concept of “Structural Diversity” of a network refers to the level of dissimilarity between the various agents acting in the system, and it is typically interpreted as the number of connected components in the network. This key property of networks has been studied in multiple settings, including diffusion of ideas in social networks and functional diversity of regions in brain networks. Here, we propose a new measure, “Structural Entropy”, as a revised interpretation to “Structural Diversity”. The proposed measure relies on the finer-grained network communities (in contrast to the network’s connected components), and takes into consideration both the number of communities and their sizes, generating a single representative value. We then propose an approach for monitoring the structure of correlation-based networks over time, which relies on the newly suggested measure. Finally, we illustrate the usefulness of the new approach, by applying it to the particular case of emergent organization of financial markets. This provides us a way to explore their underlying structural changes, revealing a remarkably high linear correlation between the new measure and the volatility of the assets’ prices over time.

A Perspective on Correlation-Based Financial Networks and Entropy Measures

“…Recently, Ricci curvature and entropy have been used to construct an economic indicator for market fragility and systemic risk [45]. Very recently, Almog et al presented a perspective on the use of entropy measures such as structural entropy [20], which is computed from the communities in correlation-based networks. Chakraborti et al computed the eigen-entropy from the eigen-vector centrality of the stocks in the correlation-based network [21].…”

“…Chakraborti et al computed the eigen-entropy from the eigen-vector centrality of the stocks in the correlation-based network [21]. Below, we discuss the structural entropy [20] and eigen-entropy [21], and compare the two measures.…”

“…The daily index return is the difference of the logarithmic values of the index (at market closure) over a period of 1 day. Thus, for the purpose of continuous monitoring of the financial market, we study the temporal evolution of the market index returns along with two entropy measures, structural entropy [20] and eigen-entropy [21]. This becomes very useful and necessary for measuring the systemic risk, market regulation and predicting downturns or crashes [22], since there often exist sizable fluctuations during crashes and bubbles.…”

Sentiment correlation in financial news networks and associated market movements

“…The network average degree reached the peak in the last quarter of 2008, which corresponds to the escalation of the financial crisis. This might be due to more companies being reported and discussed together during events of catastrophic failure in the market 4 . The increasing connectedness of the network can also be seen from its clustering coefficient and average path length shown in Figure S7(b).…”

“…While classical economic models have often been found inadequate in explaining the lower-level market dynamics 2 , there has been increasing interest and success, to varying degrees, in applying data-driven and computational modelling approaches in this context. One prominent example is the recent attempt to model financial markets as computational networks, with the individual components (for example, the individual stocks or other financial assets) being the nodes and the correlation or some other form of relation between these components being edges [3][4][5][6] . This model and its variants have been used, for example, to model the propagation of systemic risk in wider economic systems at a global scale 7 and to assess default risk propagation in sectorial networks 8 .…”