[Paper Review] COVID-19 spreading in financial networks: A semiparametric matrix regression model

Monica Billio, Roberto Casarin+2 more|arXiv (Cornell University)|Jan 2, 2021

Complex Systems and Time Series Analysis4 citations

TL;DR

This paper proposes a semiparametric Bayesian matrix regression model to analyze multilayer financial networks, capturing how COVID-19 affected interconnections among European firms via returns, volatility, risk premiums, and leverage. The model reveals heterogeneous impacts: COVID-19 increased volatility and risk premium linkages while reducing leverage connections, with more central firms experiencing greater transmission effects.

ABSTRACT

Network models represent a useful tool to describe the complex set of financial relationships among heterogeneous firms in the system. In this paper, we propose a new semiparametric model for temporal multilayer causal networks with both intra- and inter-layer connectivity. A Bayesian model with a hierarchical mixture prior distribution is assumed to capture heterogeneity in the response of the network edges to a set of risk factors including the European COVID-19 cases. We measure the financial connectedness arising from the interactions between two layers defined by stock returns and volatilities. In the empirical analysis, we study the topology of the network before and after the spreading of the COVID-19 disease.

Motivation & Objective

• To model temporal, multilayer financial networks with both intra- and inter-layer connectivity using a novel semiparametric framework.
• To assess the heterogeneous impact of the exogenous shock of the COVID-19 pandemic on financial linkages across different layers (returns, volatility, risk premiums, leverage).
• To quantify how firm centrality influences the degree to which network edges are affected by the pandemic.
• To provide a generalizable econometric framework for matrix-variate panel data applicable beyond financial networks.

Proposed method

• A Bayesian hierarchical mixture prior is used to model heterogeneity in edge responses to exogenous risk factors, including cumulative European COVID-19 cases.
• The model estimates matrix-variate response variables representing network linkages across four layers: return spillovers, volatility spillovers, risk premium spillovers, and leverage spillovers.
• Causal network structures are inferred through a semiparametric regression model that allows flexible, nonparametric estimation of coefficients while maintaining interpretability.
• The model incorporates time-varying coefficients via a multivariate regression framework with shrinkage and selection via spike-and-slab priors.
• Node-level centrality measures (in-degree, out-degree, betweenness) are used to assess firm systemic importance and its interaction with pandemic effects.
• Posterior inference is conducted using MCMC sampling on high-performance computing clusters, with posterior highest density intervals (HPDIs) used to assess significance of coefficients.

Experimental results

Research questions

• RQ1 How did the COVID-19 pandemic alter the structure of multilayer financial networks among European firms?
• RQ2 Which layers of financial connectivity—returns, volatility, risk premiums, or leverage—were most affected by the pandemic?
• RQ3 Does firm centrality moderate the impact of the pandemic on network linkages?
• RQ4 Are the effects of COVID-19 on financial networks homogeneous across firms, or do they vary systematically with firm characteristics?
• RQ5 To what extent can a semiparametric Bayesian matrix regression model capture time-varying, heterogeneous responses in financial network dynamics?

Key findings

• The COVID-19 pandemic significantly increased the probability of volatility and risk premium linkages across European financial firms, particularly in sectors like Health Care and Real Estate.
• Leverage linkages were reduced during the pandemic, indicating a contraction in balance sheet-based financial connections.
• Firms with higher in-degree (incoming linkages) were less affected by negative COVID-19 impacts on volatility, suggesting resilience to volatility shocks.
• Firms with higher out-degree (outgoing linkages) were more vulnerable to transmitting volatility shocks, indicating systemic risk amplification.
• There is a strong positive relationship between firm centrality and the number of linkages impacted by the pandemic, especially in risk premium and volatility layers where nearly half of each firm’s linkages were affected.
• Firms that moved from the first to the third tercile of betweenness centrality between January 17 and March 27, 2020, showed significant shifts in network influence, with negative impacts on edge existence uniformly affecting both low- and high-centrality firms.