The Fundamental Review of Trading Book (FRTB) sensitivity-based approach has replaced the legacy standardised measurement method as the baseline capital calculation for trading desks across Basel III jurisdictions. This shift demands that risk officers and trading heads master a granular, instrument-level methodology that captures basis risk, concentration risk, and non-linear price behaviour — all without the aggregation flexibility of the old framework.
What You Need to Know: The FRTB Sensitivity-Based Approach at a Glance
The FRTB sensitivity-based approach is a regulatory capital calculation methodology that requires banks to identify and measure risk factors underlying each trading position, then aggregate those sensitivities into standardised risk weights. Unlike the legacy approach, which relied on broad asset-class buckets and correlation assumptions, the sensitivity-based method enforces instrument-level granularity and explicit basis-risk treatment. For a trading desk holding a USD 2 million equity derivative portfolio, the old framework might have applied a single 8% risk weight; the sensitivity-based approach instead decomposes the position into delta, vega, and curvature components, each measured separately against specified risk factors and assigned distinct capital charges.
The methodology emerged from Basel Committee work post-2012 and is embedded in the final FRTB standard, with full implementation now mandatory across North America, the EU, the UK, and most Asia-Pacific regulators. The shift reflects a hard lesson from the 2008 financial crisis: aggregate correlations and model-based hedging ratios collapse precisely when banks need them most. By forcing explicit, factor-level disclosure and measurement, regulators aimed to reduce model-driven capital arbitrage and align regulatory capital more tightly with genuine economic risk.
The Three-Pillar Structure: How Capital Aggregates Under FRTB
Pillar 1: Delta Risk Capital Charge
Delta risk measures the first-order price sensitivity of a position to movements in the underlying risk factor. For a long equity index position, delta is straightforward: if the desk holds EUR 50 million notional of the EuroStoxx 50, a 1% index move generates a EUR 500,000 loss. Under FRTB, the desk must identify the specific risk factor (EuroStoxx 50 index), measure the position’s delta (EUR 50 million), and apply a standardised sensitivity delta risk weight. The regulator specifies these weights by asset class and tenor. For equity indices in the developed market bucket, the delta risk weight is typically 15%; for emerging market equity, 25%. The capital charge is then: Sensitivity × Risk Weight. So the delta capital requirement becomes EUR 50 million × 15% = EUR 7.5 million.
The challenge emerges with basis risk — the gap between the risk factor the desk is hedging against and the actual hedging instrument. If the desk uses the EuroStoxx 50 futures contract to hedge a long position in a basket of large-cap European blue chips, the basis between the index and the basket must be quantified. FRTB permits basis-risk offsets only when both the hedged position and the hedge are in the same bucket and meet tenor-matching criteria. If the desk’s basket is smaller or more concentrated than the index, the basis adjustment is capped, and unhedged basis risk flows into the capital calculation.
Pillar 2: Vega Risk Capital Charge
Vega risk captures the sensitivity of option and derivative positions to changes in implied volatility. A trader holding a long equity call position with vega of 100,000 (meaning a 1 percentage point move in implied volatility generates a EUR 100,000 P&L change) must quantify that exposure under FRTB’s vega framework. The regulator specifies vega risk weights by volatility tenor (near-term, medium-term, far-term) and asset class. For equity options in the developed market bucket, near-term vega risk weights range from 20% to 25%, medium-term from 18% to 20%, and far-term from 16% to 18%.
Critically, vega and delta are measured independently. A short 1-month, out-of-the-money call on the EuroStoxx 50 generates minimal delta (because it is out-of-the-money) but significant vega (because short-dated options are highly sensitive to volatility spikes). Under the old framework, traders could often offset vega exposure using correlation assumptions; FRTB mandates separate measurement, eliminating that aggregation benefit. The capital charge is: Vega Sensitivity × Vega Risk Weight.
Pillar 3: Curvature Risk Capital Charge
Curvature risk is the most technically demanding component. It captures the incremental loss a position would suffer if two or more risk factors move simultaneously and the delta approximation breaks down (i.e., the second-order effect, or convexity). For a long call option, if the underlying index falls sharply, the loss exceeds the linear delta prediction because the option’s delta itself declines — this is negative convexity captured as curvature risk.
FRTB’s curvature calculation is a standardised stress test, not a modelled gamma approach. The regulator specifies a stress scenario: each risk factor within a bucket is shocked by a large, defined amount (e.g., the equity index bucket receives a ±15% shock), and the maximum loss across multiple, overlapping stress scenarios is the curvature capital charge. For a desk holding long 1-month calls on EuroStoxx 50, the curvature charge would be calculated by applying the specified index stress and observing the loss in option value beyond what delta alone predicts.
Step-by-Step Capital Calculation Example: A GBP Fixed-Income Trading Desk
Consider a mid-market UK trading desk with the following simplified portfolio:
- Long GBP 100 million, 5-year UK gilt (government bond)
- Short GBP 50 million, 10-year UK gilt
- Long interest-rate swaption: 3-year tenor, 5-year underlying swap, strike 2%, notional GBP 30 million
Step 1: Identify Risk Factors. The desk’s exposures depend on three risk factors: the 5-year GBP gilt yield curve, the 10-year GBP gilt yield curve, and the 3-year-into-5-year implied volatility surface.
Step 2: Measure Delta Sensitivities. The long 5-year gilt has a duration of approximately 4.5 years; a 1 basis point (0.01%) rise in the 5-year yield causes a loss of GBP 100 million × 4.5 / 10,000 = GBP 4,500. This is the position’s delta sensitivity. The short 10-year gilt has a duration of 7 years; a 1 basis point rise in the 10-year yield causes a loss of −GBP 50 million × 7 / 10,000 = −GBP 3,500 (i.e., a gain, because the position is short). These sensitivities are then multiplied by the regulator-specified delta risk weight for interest-rate risk. For the UK, the delta risk weight for the yield-curve bucket is 0.76% (this figure is prescribed in Basel III regulations). So:
- 5-year gilt delta capital charge = GBP 4,500 × 0.76% = GBP 34.20
- 10-year gilt delta capital charge = GBP −3,500 × 0.76% = GBP −26.60
- Net delta capital for the curve positions = GBP 7.60
This simplified example already reveals a critical feature: hedges reduce but do not eliminate capital. The short 10-year gilt offsets some — but not all — of the long 5-year exposure, because the two positions respond to different points on the yield curve. The 2.5-year tenor gap cannot be collapsed under FRTB; basis risk and tenor mismatch remain in the capital calculation.
Step 3: Measure Vega Sensitivities. The swaption has a vega of approximately 150,000 GBP per 1 percentage point move in the 3-year-into-5-year implied volatility. Under FRTB, the vega risk weight for interest-rate options is 54%. Thus:
- Swaption vega capital charge = GBP 150,000 × 54% / 10,000 = GBP 810
(The division by 10,000 converts the vega sensitivity, measured in basis points, to a monetary figure.)
Step 4: Measure Curvature Risk. The swaption’s curvature is determined by shocking the 3-year-into-5-year implied volatility by a standardised amount (typically ±25% for interest-rate volatility) and observing the maximum loss. If the volatility drops 25%, the swaption loses GBP 200,000 in value beyond what vega alone predicts (because gamma is negative: the swaption loses vega as volatility falls). This is the curvature charge: GBP 200,000.
Step 5: Aggregate Capital. The total FRTB sensitivity-based capital for this desk is the sum of delta, vega, and curvature charges, subject to specified diversification limits:
- Delta capital = GBP 7.60
- Vega capital = GBP 810
- Curvature capital = GBP 200,000
- Total preliminary capital = GBP 200,817.60
This figure then undergoes a final aggregation test: if the sum of the three charges exceeds a specified regulatory threshold, a diversification benefit is applied (typically 60%–80% of the sum). However, the diversification benefit has a floor: capital cannot be less than the maximum single-risk-factor charge, preventing overaggregation.
Key Operational Challenges: Where Risk Desks Stumble
Basis Risk Quantification and Documentation
The most common pitfall is underestimating basis risk. Traders instinctively think in terms of “hedges,” but FRTB forces explicit measurement of the gap between the hedged exposure and the hedging instrument. A desk might hedge a USD 100 million notional exposure to the S&P 500 using E-mini S&P 500 futures. The basis — the difference between the spot index and the futures price, plus any tracking difference in the underlying contract — must be quantified and assigned a capital charge if it exceeds the regulator’s tolerance. If the basis is 5 basis points and the desk holds the position for 10 days, the expected loss is USD 100 million × 5 bp × 10 / 252 = USD 1,984. Under FRTB, this basis risk is not automatically offset; it flows into the curvature or residual-risk charge.
Documentation is critical because regulators now demand evidence that basis-risk hedges meet specific criteria: both legs must be in the same bucket, tenors must align within a narrow band, and the correlation assumption must be empirically defensible. Many mid-market desks discovered, upon first FRTB audit, that their hedges were documented informally or justified by approximation rather than explicit calculation.
Tenor Bucketing and Non-Parallel Curve Risk
FRTB specifies tenor buckets for yield-curve risk: typically near-term (0–3 months), short-term (3 months–2 years), medium-term (2–5 years), and long-term (5+ years). A desk with a long 3-year bond and short 5-year bond is exposed to curve twist — the differential yield between the two tenors. Under the old framework, correlation assumptions often masked this; under FRTB, the two positions are
treated as two distinct risk positions with separate capital charges — eliminating the correlation-based netting that previously reduced the combined capital requirement under the old standardised approach.
The Algoy Perspective
What most trading desks underestimate is that the FRTB sensitivity-based approach is not a more complex version of the old standardised method — it is a fundamentally different risk measurement philosophy. The firms getting this right have invested in infrastructure capable of producing daily Greeks at instrument level across every asset class. Firms retrofitting FRTB calculations onto legacy risk systems will find ongoing operational cost exceeds the initial implementation cost. The capital savings available through accurate sensitivity measurement justify the infrastructure investment.
Frequently Asked Questions
What are the three components of the FRTB SBA capital charge?
The SBA capital charge consists of the delta charge (sensitivity to movements in underlying risk factors), the vega charge (sensitivity to implied volatility) and the curvature charge (non-linear risk not covered by delta). Each component is calculated by risk class and aggregated using prescribed correlation parameters. The curvature charge is particularly capital-intensive for options books with significant gamma exposure.
How does the FRTB SBA handle correlation risk across risk classes?
The SBA applies a three-scenario framework: medium correlations using prescribed parameters, high correlations scaled up, and low correlations scaled down. The final capital charge is the maximum across all three scenarios — ensuring capital remains adequate when correlations shift under stress, as they did during the 2008 financial crisis.
When must a trading desk fall back to the SBA instead of internal models?
Desks that fail the profit and loss attribution test — comparing model-generated P&L against actual results — or fail backtesting requirements must use the SBA. Regulators may also mandate it for specific risk classes where internal models are deemed insufficiently robust. The SBA serves both as a standalone approach and as a regulatory capital floor for internal model desks.
