On the Theory of Financial Stability and Bilinear Systemic Stress Modeling

Abstract

This paper introduces an innovative framework for modeling financial stability by integrating nonlinear stress-strain dynamics, interdependent risk interactions, and regulatory countermeasures. Drawing on bilinear stress-strain relationship theory, the model incorporates macroeconomic shocks via a Hawkes process to capture the selfexciting nature of financial crises. The framework also models the interaction among credit, market, and liquidity risks and incorporates a dynamic regulatory intervention function. Stability analysis, stress amplification metrics, and dynamic stress evolution are derived to provide a robust tool for assessing systemic risk. The model is calibrated and validated using numerical experiments based on the reality of financial crisis situations, demonstrating its effectiveness in capturing shock clustering, risk amplification, and the lagged yet significant impact of central bank interventions. These results offer policymakers early warning signals and practical guidelines for mitigating systemic instability.

JEL Classification: G01, G18, C58, E58