Independent validation of a Pillar 2A concentration add-on
A European bank engaged us to validate the model behind the Pillar 2A capital add-on it holds against concentrated lending.
No framework prescribes how to size a concentration add-on, the correlation evidence is thin, and the number must still hold.
What We Provided
Assurance grounded in a rebuild, not a read-through
The add-on was rebuilt from scratch in our own modular pipeline on the same loan-level data, giving the committee an independent account of the model rather than a second opinion on its documentation.
Each component defensible on its own terms
Every component was assessed on its own construction: the granularity adjustment for single-name concentration, the multi-factor sector approach carrying intra-sector and inter-sector correlations, and the inter-portfolio correlation for geographic diversification.
Segmentation backed by evidence, not argument
The commercial real estate split decides how much of the book counts as concentrated, so Cochran-Mantel-Haenszel stratified tests, kernel density estimation and variance tests on loan-level outcomes settled whether it holds.
Knowing which assumptions move the capital
Every consequential parameter was traced back to its evidence across the model's vintages, then shifted to see how far the add-on moved, showing where more evidence is worth buying.
An independent reference point to read the number against
A simpler Herfindahl-based construction for the geographic component, needing no correlation estimate at all, gives the firm's own method something independent to be read against.
The Results
The validation found the methodology sound and appropriately conservative, and the asset and liability committee approved the report and its remediation plan ahead of the regulatory submission. The replication code and evidence pack went to the firm.
Other Case Studies
Independent validation of a Pillar 2A concentration add-on
A European bank needed to know that the capital it holds against concentrated lending would stand up to scrutiny, so it asked us for an independent view of the model behind the number.
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