Part of the 40-article FRTB Standardised Approach guide.
Featured answer: Curvature captures nonlinear loss beyond the first-order delta approximation under prescribed up and down shocks. This distinction matters for capital accuracy, risk interpretation and the evidence a supervisor or independent reviewer should expect.
The Fundamental Review of the Trading Book is easier to understand when each calculation is treated as an ordered chain rather than an isolated formula. This article explains the regulatory idea, the operational sequence and the controls that make the result defensible.
Why this FRTB topic matters
Curvature captures nonlinear loss beyond the first-order delta approximation under prescribed up and down shocks.
A reliable implementation must connect the economic position to the exact regulatory risk factor, preserve units and signs, apply the effective rule set and expose every permitted offset. The final capital number is only as reliable as that chain.
The regulatory logic
Revalue the instrument under regulatory shocks, remove the delta contribution and retain adverse nonlinear loss for aggregation.
The calculation should always be read as a sequence: define the exposure, calculate the relevant measure, apply the prescribed calibration, recognise only permitted offsets and retain enough detail to reproduce the result. Numerical parameters must come from the rulebook and jurisdictional version effective for the institution.
A practical way to think about it
A long option can benefit from one direction but still generate curvature treatment because the framework evaluates both shock directions.
This example is conceptual rather than a substitute for a regulated calculation. Its purpose is to show where judgement, data and aggregation enter the process, and why economic hedging does not automatically create the same regulatory offset.
Step-by-step implementation
- Confirm scope and regulatory classification before calculating any sensitivity or capital amount.
- Identify the valuation risk drivers and map them to the prescribed regulatory risk factors.
- Calculate measures using controlled market data, valuation models, units and sign conventions.
- Apply the current jurisdictional risk weights, correlations, buckets and special treatments.
- Aggregate at factor, bucket, risk-class and total-capital level while retaining the audit trail.
- Reconcile results, investigate exceptions and approve the run under the bank control framework.
Controls that make the result defensible
Use full revaluation, consistent market data and independent tests that delta subtraction and shock direction are correct.
- Completeness: every in-scope position reaches exactly the required capital components.
- Accuracy: sensitivities, mappings, parameters and aggregation are independently testable.
- Timeliness: market data, reference data and regulatory versions are effective for the run date.
- Explainability: material capital movements can be traced to economic or controlled data changes.
Common implementation mistakes
Replacing full revaluation with gamma shortcuts without justification can misstate path-dependent or strongly nonlinear products.
A useful review question is whether a knowledgeable person could reproduce the treatment from the trade terms, market data, regulatory mapping and versioned parameter set without undocumented judgement. If not, the process is not yet production-grade.
Key takeaways
- Curvature captures nonlinear loss beyond the first-order delta approximation under prescribed up and down shocks.
- FRTB permits diversification only through its defined hierarchy.
- Mapping, units and product coverage are as important as the final aggregation formula.
- Local rules and effective dates must be verified before using any numerical calibration.
Frequently asked questions
Is this relevant only to banks using internal models?
No. The standardised approach is a standalone capital methodology, a fallback and an important benchmark even where internal models are used.
Can a bank use its own correlations or risk weights?
Not for the regulatory standardised calculation unless the applicable local rule explicitly permits an alternative. Prescribed parameters are central to comparability.
Does good economic hedging always remove capital?
No. Recognition depends on regulatory risk-factor identity, bucket structure, correlations and component-specific netting rules.
Conclusion
Curvature captures nonlinear loss beyond the first-order delta approximation under prescribed up and down shocks. The durable implementation principle is simple: classify correctly, measure consistently, apply the prescribed framework exactly and make every material judgement traceable.
Primary sources
- Basel Committee, MAR20 - Standardised approach: general provisions and structure
- Basel Committee, MAR21 - Standardised approach: sensitivities-based method
Related FRTB reading
Educational material, not legal, regulatory or investment advice. Verify local law, technical standards and effective dates before implementation.