Samal Areejit, Pharasi Hirdesh K, Ramaia Sarath Jyotsna, Kannan Harish, Saucan Emil, Jost Jürgen, Chakraborti Anirban
The Institute of Mathematical Sciences (IMSc), Chennai 600113, India.
Homi Bhabha National Institute (HBNI), Mumbai 400094, India.
R Soc Open Sci. 2021 Feb 24;8(2):201734. doi: 10.1098/rsos.201734.
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.
金融市场的复杂性源于交易股票的主体之间的战略互动，这种互动表现为股价之间活跃的相关模式。在过去几十年里，复杂的金融市场常常被表示为网络，其相互作用的节点对是股票，由表示相关强度的边连接。然而，我们经常会遇到三个或更多节点的组内相互作用，这些不能简单地用成对相互作用来描述，我们还需要考虑这些相互作用之间的关系。直到最近，研究人员才开始关注复杂金融系统的高阶架构，这可以显著提高我们估计系统性风险的能力，以及从市场效率方面衡量金融系统的稳健性。受几何启发的网络度量，如奥利维耶 - 里奇曲率和福尔曼 - 里奇曲率，可用于捕捉网络脆弱性并持续监测金融动态。在此，我们探索这种离散里奇曲率在刻画金融系统结构方面的效用，并进一步将它们评估为市场不稳定的通用指标。为此，我们研究了一组包含美国标准普尔500指数和日本日经225指数的股票在长达32年期间的日回报率，并监测以边为中心的网络曲率的变化。我们发现，不同的几何度量很好地捕捉了市场的系统层面特征，因此我们可以区分正常或“照常营业”时期与所有主要的市场崩溃。这在金融系统的战略设计和监管市场以应对金融不稳定方面可能非常有用。
