Systemic Risk in a Multilayer Financial Network: A Criticality-Based Perspective

Banks and firms are connected through multiple credit relationships that can transmit financial shocks across sectors, amplify default contagion, and ultimately lead to system-wide collapse. Understanding systemic risk therefore requires not only examining default contagion mechanisms but also characterizing system-wide collapse. To this end, we construct a three-layer financial network model and examine its response to exogenous shocks. Under the baseline configuration, numerical simulations reveal pronounced bimodal distributions of bankruptcy fractions, indicating that the sharp increase in average bankruptcy fractions mainly reflects a shift in the relative frequencies of limited-contagion and system-wide collapse states. Susceptibility and finite-size analyses provide further evidence of phase-transition-like behavior. Building on these findings, we characterize systemic risk using complementary measures of collapse likelihood, shock tolerance, and financial damage, measured by system-wide collapse probability, collapse thresholds, and layer-specific loss ratios, respectively. Matched counterfactual experiments show that two-layer configurations without endogenous interfirm credit propagation have higher system-wide collapse thresholds than the three-layer model under both recovery-matching conventions, although the increase is much larger under recovery-rate matching than under recovery-amount matching. Parameter experiments further show how balance-sheet composition, interfirm link formation, and credit exposure are associated with shock tolerance.