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The SARS-CoV-2 epidemics outbreak has shocked global financial markets, inducing policymakers to put in place unprecedented interventions to inject liquidity and to counterbalance the negative impact on worldwide financial systems. Through the lens of statistical physics, we examine the financial volatility of the reference stock and bond markets of the United States, United Kingdom, Spain, France, Germany and Italy to quantify the effects of country-specific socio-economic and political announcements related to the epidemics. Main results show that financial markets exhibit heterogeneous behaviours towards news on the epidemics, with the Italian and German bond markets responding with major delays to shocks. Additionally, credit markets tend to be slower than equity markets in adjusting prices after shocks, hence being slower at incorporating the effects of such news.

We introduce an indicator that aims to detect the emergence of market instabilities by quantifying the intensity of self-organizing processes arising from stock returns’ co-movements. In financial markets, phenomena like imitation, herding and positive feedbacks characterize the emergence of endogenous instabilities, which can modify the qualitative and quantitative behavior of the underlying system. The impossibility to formalize ex-ante the dynamic laws that rule the evolution of financial systems motivates the use of a parsimonious synthetic indicator to detect the disruption of an existing equilibrium configuration. Here we show that the emergence of an interconnected sub-graph of stock returns co-movements from a broader market index is a signal of an out-of-equilibrium transition of the underlying system. To test the validity of our approach, we propose a model-free application that builds on the identification of up and down market phases.

Financial markets are complex systems where investors interact using competing strategies that generate behaviours in which herding and positive feedbacks may lead to endogenous instabilities. This paper develops a novel methodology to detect the emergence of such phases by quantifying the intensity of self-organizing processes arising from stock returns’ co-movements and self-similarities. Our methodology identifies a group of stocks, the Leading Temporal Module, whose statistical properties reflect the transition of the market into a crisis state. We define a topological indicator of the emergence of market discontinuity based on the autocovariance of the stocks in the Leading Temporal Module and on the ratio between the stocks’ correlations within this group and the correlations between these stocks and those outside the leading module. This indicator provides early-warning market signals useful for policy-makers and investors by mapping the evolution of the topological properties of the leading module in different points in time.

When resources are shared between interacting networks, the importance of each node depends strongly on how collaborative or competitive each sub-network is. In this paper, we develop a new method of measuring centrality in the complex network of patent citations that can take political borders into account, where the national benefit of domestic citations relative to foreign citations can be controlled by a free parameter. We find that while some patent classes are of high importance both in the global and the domestic economy, there often exist patent classes in individual countries that are more central nationally than in global economy. We characterize the most important classes globally and domestically for six different nations, and describe their robustness to various perturbations to the model and to noise.