Transient Amplification and Systemic Risk in Interbank Networks: A Non-Normal Operator Approach

Abstract Interbank financial systems are characterized by complex networks of obligations and liquidity dependencies. Classical stability analysis relies on equilibrium assumptions and spectral criteria, which do not capture transient amplification effects in non-normal systems. In this work, interbank networks are modeled as non-normal dynamical systems governed by asymmetric exposure matrices. It is shown that even spectrally stable systems may exhibit large transient amplification, leading to liquidity stress propagation and cascade failures. A dimensionless instability functional is introduced to quantify the interaction between amplification and system capacity. A finite-time instability condition is established, demonstrating that systemic risk is governed by transient dynamics rather than asymptotic behavior. Numerical examples illustrate how localized shocks propagate through interbank networks, producing amplification effects that may exceed system capacity. The framework provides a mathematically consistent approach to systemic risk analysis and offers a basis for improved stress-testing methodologies.