Structural Z-score

The central hypothesis of this study is that the traditional accounting-based Z-score fails to provide a reliable and forward-looking measure of bank default risk because it relies on an unrealistic definition of default, ignores balance-sheet and income-statement dynamics, and neglects persistence in bank risk drivers. We hypothesise that a structural Z-score, grounded in prudential solvency constraints and incorporating memory in risk dynamics, provides a more economically meaningful and empirically informative measure of bank risk.

The dataset consists of annual balance-sheet and income-statement data for eight systemically important European banks over the period 1997–2024 (exact coverage may vary slightly by institution). The sample includes Banco Santander, BNP Paribas, Crédit Agricole, Deutsche Bank, Lloyds Banking Group, Société Générale, UBS, and UniCredit.
The core variables include: total income, total expenses, total profit, total assets, total capital adequacy, risk-weighted assets (RWAs), and solvency ratio.
All variables are expressed in million Euros and were extracted from Refinitiv LSEG dababase and from annual reports and regulatory disclosures of banks.

The repository contains Python scripts implementing the full estimation procedure:
- nonparametric Beta-kernel density estimation with bounded support,
- memory-based conditional weighting,
- computation of conditional expectations via numerical integration,
- fixed-point iterative procedure ensuring internal consistency,
- computation of structural Z-scores under a Geometric Brownian Motion assumption for income;
Replication scripts allowing users to reproduce all figures and results reported in the paper.

The data show that the proposed structural Z-score exhibits dynamics that differ markedly from the traditional Z-score and often delivers opposite signals regarding bank risk. While the traditional Z-score frequently reaches implausibly high values, the structural Z-score remains economically interpretable and closely linked to prudential solvency conditions. The results highlight the central role of predicted expenses, predicted risk-weighted assets, and capital adequacy in shaping bank default risk, as well as the importance of persistence in these variables.

The Python codes are designed for full reproducibility and can be reused to:
- compute structural Z-scores for other banks or countries,
- analyse the role of persistence in bank risk dynamics,
- extend the framework to alternative default definitions or stochastic processes.

All files are documented and organised to facilitate replication and further methodological or empirical extensions.