A probabilistic and graph-theoretic approach to the analysis of credit and liquidity risk contagion with delay effects in a banking system

Abstract

This paper proposes a probabilistic interpretation of a delayed banking contagion model driven by the interaction between credit risk and liquidity risk. Instead of restricting the analysis to a local study around an equilibrium, the banking system is represented by a weighted directed graph whose vertices are banks and whose edges describe bilateral exposures. This framework captures bank heterogeneity, exposure intensity, network structure, and delayed transmission effects in a unified way. Each institution evolves among four financial states: healthy, exposed to credit risk, exposed to liquidity risk, and defaulted. Transitions between these states are described by probabilities depending on neighborhood conditions, exposure weights, and delay parameters. We further introduce structural indicators, including centrality measures and a synthetic systemic vulnerability index, to identify the institutions most likely to amplify contagion. Numerical simulations show how small changes in transmission and recovery mechanisms may shift the system from a contained stress regime to a generalized crisis.