Abstract
In this mini-review, we critically examine the recent work done on correlation-based networks in financial systems. The structure of empirical correlation matrices constructed from the financial market data changes as the individual stock prices fluctuate with time, showing interesting evolutionary patterns, especially during critical events such as market crashes, bubbles, etc. We show that the study of correlation-based networks and their evolution with time is useful for extracting important information of the underlying market dynamics. Also, we present our perspective on the use of recently-developed entropy measures, such as structural entropy and eigen-entropy, for continuous monitoring of correlation-based networks.
Highlights
Network science [1,2,3,4] has emerged as an important tool for studying different complex phenomena– spread of infectious diseases [5, 6], economic production [7], construction of robust sustainable infrastructure and technological networks [8], processing human information [9], innovation diffusion [10], detection of financial crashes [11,12,13], etc
In this mini-review, we focus on the role of network science in understanding complex financial markets
It is noteworthy that financial networks are naturally “weighted,” as each link bears a numeric value representing the correlation between the nodes
Summary
Network science [1,2,3,4] has emerged as an important tool for studying different complex phenomena– spread of infectious diseases [5, 6], economic production [7], construction of robust sustainable infrastructure and technological networks [8], processing human information [9], innovation diffusion [10], detection of financial crashes [11,12,13], etc. Our aims are two-fold: (i) To uncover the structure of the complex interactions among stocks at a particular period of time (static picture) through correlation-based networks, where the nodes represent the stocks in the financial market, and the links represent the interaction strengths of co-movements of stocks (as measured by correlations). For this purpose, one starts with computing the crosscorrelations among stock price returns and constructs any of the correlation-based networks– Minimum Spanning Tree (MST) [14, 15], Threshold Network [16], Planar Maximally Filtered Graph (PMFG) [17], etc. The understanding of the stock market dynamics can be very important for practical applications like portfolio optimization, risk management, etc. (ii) To continuously
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