FRM Exam Part II · Fundamental Review of the Trading Book

FRTB Standardized Approach: Sensitivities-Based Method Explained

Updated 11 October 2026 · Fact-checked

The FRTB standardized approach adds three parts: the sensitivities-based method (delta, vega and curvature charges across seven risk classes), the default risk charge, and the residual risk add-on. To solve questions, weight sensitivities by risk weights, aggregate within buckets using correlations, then across buckets, and take the worst of three correlation scenarios.

Understand Standardized Approach (Sensitivities-Based Method)

The standardized approach (SA) is the Basel FRTB rulebook that every bank must calculate, even if it uses internal models. It is also the fallback and the floor-like benchmark for desks that fail internal model tests. It does not use a bank's own VaR or Expected Shortfall model. Regulators set the risk weights and correlations.

The capital charge has three parts. First, the sensitivities-based method (SBM) captures market risk using delta, vega and curvature. Second, the default risk charge (DRC) captures jump-to-default risk on credit and equity positions. Third, the residual risk add-on (RRAO) is a simple charge on exotic or hard-to-model risks. Total SA capital = SBM + DRC + RRAO.

The SBM works by risk class. The seven classes are: general interest rate risk (GIRR), credit spread risk for non-securitisations, credit spread risk for securitisations (non-correlation trading), credit spread risk for the correlation trading portfolio, equity, commodity and FX. Within each class, risk factors sit in buckets, for example currencies for GIRR, or sector and market-cap groups for equity.

The delta charge starts from a sensitivity to each risk factor, such as PV01 for rates. You multiply it by a prescribed risk weight to get a weighted sensitivity. Vega does the same for implied volatility. Curvature captures what delta misses for options: the loss from a larger shock beyond the linear estimate.

Aggregation is the core skill. Inside a bucket, risk factors are combined with prescribed correlations, so offsetting positions partly cancel. Across buckets, a second correlation applies. Because correlations are uncertain, the bank runs three scenarios (high, medium, low) and takes the highest capital result. This gives a conservative, rule-based number.

Key formulas to remember

Weighted sensitivity: WS_k = RW_k × s_k; s_k is the net sensitivity to risk factor k (for example PV01 for GIRR). RW_k is the prescribed risk weight.
Within-bucket aggregation: K_b = √( max(0, Σ WS_k² + Σ Σ ρ_kl × WS_k × WS_l) ), for k ≠ l; Used for delta and vega. ρ_kl is the prescribed correlation between risk factors in the same bucket.
Across-bucket aggregation: Charge = √( Σ K_b² + Σ Σ γ_bc × S_b × S_c ), for b ≠ c; S_b is the sum of weighted sensitivities in bucket b (K_b is the cap/floor in the alternative specification). γ_bc is the cross-bucket correlation.
Three correlation scenarios: High: ρ × 1.25, capped at 100% | Medium: ρ | Low: max(2ρ − 100%, 75% × ρ); Apply to both ρ and γ. Compute capital under each scenario and use the highest result.
GIRR tenor correlation: ρ = max( e^(−θ × |T_k − T_l| ÷ min(T_k, T_l)), 40% ), with θ = 3%; Between different tenors of the same curve in the same currency. Cross-currency bucket correlation is 50%.
Vega risk weight: RW = min( RW_σ × √LH ÷ √10, 100% ); LH is the liquidity horizon of the risk class, in days. Vega sensitivity = vega × implied volatility.
Curvature risk position: CVR_up = −[ V(x + shock) − V(x) − RW_curv × s ]; CVR_down = −[ V(x − shock) − V(x) + RW_curv × s ]; s is the delta sensitivity of the instrument. A positive CVR is a loss. Within-bucket curvature aggregation uses ρ squared. Curvature applies to instruments with optionality.
Jump-to-default (JTD): Long: max(LGD × notional + P&L, 0) | Short: min(LGD × notional + P&L, 0), with notional negative for shorts; Prescribed LGD: 75% senior debt, 100% non-senior and equity, 25% covered bonds.
DRC bucket charge: DRC_b = max(0, Σ RW × net long JTD − WtS × Σ RW × |net short JTD|); WtS = Σ net long JTD ÷ (Σ net long JTD + Σ |net short JTD|). Netting only across the same obligor. Bucket charges are summed with no diversification.
Residual risk add-on: RRAO = 1.0% × gross notional (exotic underlyings) + 0.1% × gross notional (other residual risks); Applies to instruments with exotic underlyings or other residual risks, such as gap, correlation or behavioural risks.
Total SA capital: Capital = SBM + DRC + RRAO; SBM is the highest of the three correlation scenario results.

How to solve Standardized Approach (Sensitivities-Based Method) questions

Use this order for any FRTB standardized approach question. It tells you quickly which component the question is testing.

1Identify the component: SBM (delta, vega or curvature), DRC or RRAO. Then identify the risk class and bucket.
2Compute or read the sensitivity for each risk factor. For GIRR use PV01 per tenor. For vega use vega × implied volatility.
3Multiply by the risk weight to get weighted sensitivities. Keep the signs; shorts and hedges are negative.
4Aggregate within each bucket with the formula K_b = √(ΣWS² + ΣΣρ·WS·WS). Check that the sign of the cross term follows the signs of the WS values.
5Aggregate across buckets with the γ correlations. Note whether the question asks for the bucket charge or the risk class charge.
6If the question mentions scenarios, repeat with high, medium and low correlations. Take the maximum.
7Add DRC (no diversification across buckets) and RRAO (flat percentage of gross notional) if the question asks for total SA capital.
8Sanity check: a charge should not exceed the sum of absolute weighted sensitivities, and perfect correlation should give exactly that sum.

Quickest way: Two-factor shortcut and elimination

When to use it: Use it when the question gives two or three weighted sensitivities and four numeric options.

Compute the sum of absolute weighted sensitivities. This is the ceiling (ρ = 100%).
Compute the root of the sum of squares. This is the value at ρ = 0.
The true answer lies between them when correlations are positive and the positions have the same sign. If the positions offset, it lies below the root of the sum of squares at ρ = 0.
Eliminate options outside that range, then do the exact calculation only for what remains.
For DRC, compute WtS first. It lies between 0 and 1. A DRC above the gross long charge (Σ RW × long JTD) is always wrong.

Common mistakes in Standardized Approach (Sensitivities-Based Method)

Taking the average of the three correlation scenarios, or using only the medium scenario.
Students treat the scenarios like a sensitivity analysis.
Fix: Compute capital under each scenario and take the highest. The charge is conservative by design.
Applying weights before netting sensitivities, or netting across different tenors or buckets before weighting.
It feels natural to net offsetting positions first.
Fix: Net sensitivities only for the same risk factor. Then weight. Then use correlations to give partial offset across different factors.
Using ρ instead of ρ squared in curvature aggregation.
Delta, vega and curvature all share the same aggregation layout.
Fix: Delta and vega use ρ. Curvature uses ρ squared inside the bucket. Remember that curvature is the option-convexity charge.
Netting JTD across different obligors, or diversifying the DRC across buckets.
Students carry over the diversification logic of the SBM.
Fix: Net only positions on the same obligor. Sum bucket charges simply. Hedges across obligors only enter through the WtS ratio within a bucket.
Applying the RRAO to the market value or to net notional.
Charges are usually linked to risk positions, not notional.
Fix: RRAO is a percentage of gross notional: 1.0% for exotic underlyings and 0.1% for other residual risks.
Treating the SA as an internal model with a 97.5% Expected Shortfall.
FRTB is associated with the shift from VaR to ES.
Fix: The SA uses no statistical confidence level. It uses regulator-set risk weights, correlations and shocks. Liquidity horizons are built into the risk weights.

Worked examples

Example 1

A USD GIRR bucket has two delta exposures. 2-year PV01 is USD 8,000 per basis point (long). 5-year PV01 is −USD 5,000 per basis point. Risk weights are 1.3% for the 2-year and 1.1% for the 5-year. Use θ = 3%. Find the bucket delta charge K_b.

Show the solution

Convert the risk weights to basis points: 1.3% = 130 bp and 1.1% = 110 bp.
WS(2y) = 130 × 8,000 = USD 1,040,000.
WS(5y) = 110 × (−5,000) = −USD 550,000.
Correlation: ρ = e^(−0.03 × |5 − 2| ÷ 2) = e^(−0.045) ≈ 0.956. This is above the 40% floor.
Work in USD millions: WS1² = 1.0816 and WS2² = 0.3025. Sum = 1.3841.
Cross term: 2 × 0.956 × 1.04 × (−0.55) = −1.0937.
Inside the root: 1.3841 − 1.0937 = 0.2904.
K_b = √0.2904 ≈ 0.5389 million.

Answer: K_b is about USD 538,900. The two exposures largely offset because the tenors are highly correlated.

Example 2

In the corporate bucket, a bank holds a long position in obligor A (rated BBB, risk weight 6%): senior bond, notional USD 10 million, market value equal to notional. It also holds a short position in obligor B (rated BB, risk weight 15%): senior bond, notional USD 4 million, market value equal to notional. Compute the DRC for this bucket.

Show the solution

Senior LGD is 75%. P&L from the notional is zero because market value equals notional.
JTD for A (long) = 0.75 × 10 million + 0 = USD 7.5 million.
JTD for B (short) = −(0.75 × 4 million) + 0 = −USD 3 million.
The obligors differ, so no netting is possible. Net long = 7.5 and net short = 3 (in millions).
WtS = 7.5 ÷ (7.5 + 3) = 0.7143.
Long charge: 6% × 7.5 = 0.45 million.
Short offset: 0.7143 × 15% × 3 = 0.3214 million.
DRC = max(0, 0.45 − 0.3214) = 0.1286 million.

Answer: The bucket DRC is about USD 128,600. The short on B offsets the long on A only partly because of the WtS scaling and the risk weight difference.

Exam tips

Questions often ask which component captures a risk: curvature for option convexity, DRC for jump-to-default, RRAO for exotic payoffs. Match the risk to the charge first.
Know the sign logic. Offsetting weighted sensitivities with positive correlation reduce the bucket charge. If your charge exceeds the sum of absolute weighted sensitivities, you have made an error.
Memorise the structure, not every risk weight: seven risk classes, three charges, three correlation scenarios, take the maximum. Exact weights are normally given in the question.
For DRC, always compute the WtS ratio and check netting only within the same obligor. Do not diversify across buckets.
Be ready for conceptual MCQs: the SA is the fallback for desks that fail the internal model approach, and the SA charge is computed for all trading desks by banks using internal models.

Practice questions from Fundamental Review of the Trading Book

Standardized Approach (Sensitivities-Based Method): frequently asked questions

What are the three parts of the FRTB standardized approach?

The sensitivities-based method, the default risk charge and the residual risk add-on. The SBM itself has delta, vega and curvature components across seven risk classes. The total capital is the sum of the three parts.

Why does FRTB use three correlation scenarios?

Correlations are unstable, especially in stress. Regulators therefore require capital under high, medium and low correlation assumptions and take the highest result. This makes the charge conservative without relying on a bank's own model.

What does the curvature charge capture?

It captures the loss from a large price shock that delta alone does not capture, which matters for options and other non-linear instruments. You revalue the position under an up and a down shock and compare it with the delta approximation. The worse of the two outcomes drives the charge.

How is the residual risk add-on different from the other charges?

It is a simple percentage of gross notional rather than a sensitivity calculation. It is 1.0% for instruments with exotic underlyings and 0.1% for other instruments carrying residual risks. It covers risks that the sensitivities-based method cannot capture.