Network geometry and market instability

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.

Network-centric Indicators for Fragility in Global Financial Indices

“…Note that bubbles are not easy to detect. In fact, our proposition is that holistic approaches with network measures, both node-and edge-based measures, including geometric curvatures, may help us to better detect and distinguish the bubbles from market crashes, as also pointed out in recent contributions [26,49]. In sum, we find that during a normal period the network of global market indices is less connected, very modular, and heterogeneous, whereas, during a fragile period, the network is highly connected, less modular, and more homogeneous.…”

“…To the best of our knowledge, this is the first study employing edge-based discrete Ricci curvatures to networks of global financial indices. Our recent work underscores the utility of edge-based curvature measures in the analysis of networks of stocks [49] or global financial indices. In future, curvature measures may also find application in other financial networks including Banking networks [50].…”

“…As far as we know, this work is the first to use threshold networks of MST plus edges with a correlation higher than a specified threshold, to study the temporal evolution of relationships between global financial market indices. In contrast, such threshold networks based on MST have been used earlier to study the structure of stock market networks [29,49]. While MST has a tree structure without loops or cycles, PMFG or threshold network permits loops or cycles.…”

Graph Ricci Curvatures Reveal Atypical Functional Connectivity in Autism Spectrum Disorder

“…A MST is particularly useful for network-based analyses since it ensures that the resulting network is always connected. Similar network construction approaches involving spanning trees have previously been used for financial networks [41,42] and brain FCNs [72].…”

“…Various nonequivalent definitions of graph Ricci curvature have been proposed [35][36][37][38][39] with an aim to capture the key properties of the classical Ricci curvature. Different notions of graph Ricci curvature have found applications in diverse areas, such as differentiating gene co-expression networks of cancer cells and healthy cells [40], identifying crashes and bubbles in financial networks [41,42], and community detection in complex networks [43,44]. Ollivier-Ricci curvature (ORC) [37] and Forman-Ricci curvature (FRC) [36,38] are two widely used notions of graph Ricci curvature.…”