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Systemic risk: a network approach

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Abstract

We propose a new measure of systemic risk based on interconnectedness, defined as the level of direct and indirect links between financial institutions in a correlation-based network. Deriving interconnectedness in terms of risk, we empirically show that within a financial network, indirect links are strengthened during systemic events. The relevance of our measure is illustrated at both local and global levels. Our framework offers policymakers a useful toolbox for exploring the real-time topology of the complex structure of dependencies in financial systems and for measuring the consequences of regulatory decisions.

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Notes

  1. Systemic risk measures are described in “Appendix”.

  2. See also Amini et al. (2016) and Barucca et al. (2020) for a mathematical approach of contagion mechanisms.

  3. The results appear to be robust to the use of other models to model the time-varying correlation.

  4. About the necessary and sufficient conditions for covariance and correlation matrices, see Stefanica (2014), Chapter 7, pp. 200–204.

  5. We denote by \(C_m\) the matrix that has gone through the process of transformations from the initial correlation matrix C: \(\psi \circ \psi ^{-1}\). We denote by \(C_m^{*}\) matrix \(C_m\) that has been through the whole process: \(\psi \circ \phi \circ \psi ^{-1}\) (i.e., the process that silences direct links that are weaker than indirect links and replaces them by the latter).

  6. \(O_{B}(\mathbb {R}^{+})\) denotes the set of positive orthogonal matrices.

  7. ECB website’s direct https://www.ecb.europa.eu/press/pr/date/2017/html/ecb.pr170628.en.html.

  8. The correlation matrices’ transformation is computed using R package “highfrequency” by Boudt et al. (2014).

  9. Considering the low ratio of instances of 1 to instances of 0 exhibited by the recession dummy, logit models are preferable to probit models. See Naceur et al. (2019).

  10. CRESPR, LIQSPR and YIESPR are defined as the change in the credit spread (the BAA corporate bond rate minus the 10Y treasury bond rate), the change in the liquidity spread (the 3M treasury bill rate minus the ECB refinancing rate) and the change in the yield spread (the 10Y treasury bond rate minus the 3M treasury bond rate).

  11. Interconnectedness is one of the five systemic risk categories used by the Basel Committee in its scoring approach to identify and regulate SIFIs since 2011. See Benoit et al. (2019) for an overview of this framework.

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  1. Aix-Marseille Univ., CNRS, EHESS, Centrale Marseille, AMSE, Marseille, France

    Jean-Baptiste Hasse

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Correspondence to Jean-Baptiste Hasse.

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The author would like to thank Sylvain Benoit, Renaud Bourlès, Yann Bramoullé, Éric Girardin, Kasper Roszbach and seminar participants at the AMSE Finance Seminar (Aix-Marseille University - AMSE, 2021), 6th INFINITI conference (University of Glasgow, 2019), the 9th FEBS conference (University of Economics, Prague, 2019), the XIIth MIFN annual meeting (Université Catholique de Louvain, 2018), the XIth MIFN annual meeting (University of Shandong, 2017), the 2nd symposium “Financial Risk & Network Theory” (University of Cambridge, 2016), the 2nd Banque de France - University College London workshop “Impact of Uncertainty Shocks on the global Economy” (University College London, 2016), and the 2nd van Gogh grant meeting (Institut Louis Bachelier, 2015) for comments received regarding the preliminary results. This research has been conducted with the research program “Risk Management, Investment Strategies and Financial Stability” under the aegis of the Institut Louis Bachelier, a joint initiative with insti7.

Appendix

Appendix

See Table 6.

Table 6 Systemic risk measures
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Hasse, JB. Systemic risk: a network approach. Empir Econ 63, 313–344 (2022). https://doi.org/10.1007/s00181-021-02131-2

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