Determining Insolvency Regions in Banks: A Stochastic Dynamic Approach Integrating Liquidity and Credit Risk

2026-07-19

AI Summary

This study addresses the endogenous insolvency risk banks face due to the nonlinear interaction between liquidity and credit risks—a dynamic often treated in isolation by existing literature. The authors develop a continuous-time structural model that embeds Basel III’s Liquidity Coverage Ratio (LCR) and Net Stable Funding Ratio (NSFR) constraints within a stochastic dynamic control framework. By solving the associated Hamilton–Jacobi–Bellman (HJB) equation, they precisely characterize the bankruptcy boundary and, for the first time, explicitly uncover the feedback mechanism linking liquidity shocks, regulatory constraints, and balance sheet adjustments. Calibrated using granular balance sheet data, the model yields an analytically tractable proxy function enabling real-time monitoring. Empirical validation on Iranian banking data reveals pronounced nonlinear threshold effects under joint risk exposure, offering regulators a theoretically rigorous yet practically applicable tool for stress testing and early-warning systems.

Abstract

We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead to endogenous insolvency. By incorporating Basel III regulatory requirements (LCR and NSFR) into a stochastic optimal control framework, we solve for the exact insolvency boundary using the Hamilton-Jacobi-Bellman (HJB) equation. To bridge the gap between theoretical complexity and supervisory practice, we derive and validate a surrogate analytical approximation function that allows for real-time monitoring. Calibrated using granular balance-sheet data from the Iranian banking sector, our model reveals significant non-linear threshold effects: the joint occurrence of liquidity stress and credit portfolio defaults disproportionately accelerates the transition toward insolvency compared to their individual effects. The proposed surrogate function offers supervisors a computationally efficient tool for stress testing and early warning systems. Our findings provide novel insights into financial frictions in emerging markets and offer a rigorous framework for integrated risk management.

Problem

• insolvency regions
• liquidity risk
• credit risk
• Basel III
• financial frictions

Innovation

• stochastic optimal control
• Hamilton-Jacobi-Bellman equation
• liquidity-credit risk interaction
• insolvency boundary
• Basel III regulatory constraints