Measuring the stability of the banking system: capital and liquidity at risk with solvency-liquidity interactions

This study develops a stochastic balance sheet based microstructural banking model to quantify the dynamic interplay between solvency and liquidity risks – two traditionally distinct dimensions in stress testing. By incorporating endogenous bank reactions, feedback loops, and amplification mechanisms, the model captures how management responses to shocks can escalate financial distress, potentially leading to insolvency and illiquidity. We apply the model to granular loan and security exposure data from UK banks over 2015–24, estimating capital and liquidity at risk and deriving a systemic default probability indicator. Results indicate an average one-year bank default probability of 0.7%, consistent with market-implied estimates but diverging during stress episodes. Amplification effects, driven by balance sheet constraints and behavioural responses, account for approximately one third of default risk on average. Counterfactual analyses further evaluate the effectiveness of capital requirements and identify optimal capital levels under hypothetical stress scenarios.