The analysis of systemic risk often revolves around examining various measures utilized by practitioners and policymakers. These measures typically focus on assessing the extent to which external events can impact a financial system, without delving into the nature of the initial shock. In contrast, our approach takes a symmetrical standpoint and introduces a set of measures centered on the quantity of external shock that the system can absorb before experiencing deterioration. To achieve this, we employ a linearized version of DebtRank, which facilitates a clear depiction of the onset of financial distress, thereby enabling accurate estimation of systemic risk. Through the utilization of spectral graph theory, we explicitly compute localized and uniform exogenous shocks, elucidating their behavior. Additionally, we expand the analysis to encompass heterogeneous shocks, necessitating computation via Monte Carlo simulations. We firmly believe that our approach is both comprehensive and intuitive, enabling a standardized assessment of failure risk in financial systems.

• Received 14 April 2023
• Accepted 13 September 2023

DOI:https://doi.org/10.1103/PhysRevE.108.044303