Abstract
The complexity of financial markets arise from the strategic interactions among agents trading stocks, which manifest in the form of vibrant correlation patterns among stock prices. Over the past few decades, complex financial markets have often been represented as networks whose interacting pairs of nodes are stocks, connected by edges that signify the correlation strengths. However, we often have interactions that occur in groups of three or more nodes, and these cannot be described simply by pairwise interactions but we also need to take the relations between these interactions into account. Only recently, researchers have started devoting attention to the higher-order architecture of complex financial systems, that can significantly enhance our ability to estimate systemic risk as well as measure the robustness of financial systems in terms of market efficiency. Geometry-inspired network measures, such as the Ollivier–Ricci curvature and Forman–Ricci curvature, can be used to capture the network fragility and continuously monitor financial dynamics. Here, we explore the utility of such discrete Ricci curvatures in characterizing the structure of financial systems, and further, evaluate them as generic indicators of the market instability. For this purpose, we examine the daily returns from a set of stocks comprising the USA S&P-500 and the Japanese Nikkei-225 over a 32-year period, and monitor the changes in the edge-centric network curvatures. We find that the different geometric measures capture well the system-level features of the market and hence we can distinguish between the normal or ‘business-as-usual’ periods and all the major market crashes. This can be very useful in strategic designing of financial systems and regulating the markets in order to tackle financial instabilities.
Highlights
Science had thrived on the method of reductionism—considering the units of a system in isolation, and trying to understand and infer about the whole system
We show the evolution of the discrete curvatures in threshold networks over the 32-year period
The market becomes extremely correlated and volatile during a crash, but a bubble is even harder to detect as the volatility is relatively low and only certain sectors perform very well but the rest of the market behaves like normal or ‘business-as-usual’
Summary
Science had thrived on the method of reductionism—considering the units of a system in isolation, and trying to understand and infer about the whole system. We expand the study of geometry-inspired network measures for characterizing the structure of the financial systems to four notions of discrete Ricci curvature, and evaluate the curvature measures as generic indicators of the market instability. A major goal of this research is to evaluate different notions of discrete Ricci curvature for their ability to unravel the structure of complex financial networks and serve as indicators of market instabilities. We find using these geometric measures that there are succinct and inherent differences in the two markets, USA S&P-500 and Japan Nikkei-225 These new insights will help us to understand tipping points, systemic risk, and resilience in financial networks, and enable us to develop monitoring 4 tools required for the highly interconnected financial systems and perhaps forecast future financial crises and market slowdowns
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