FRTB GIRR delta charge
The standardised approach does not net positions by magic: it weights each tenor sensitivity, correlates the tenors, and aggregates. This is the general interest rate risk delta charge for one currency bucket, with the correlation matrix visible so the hedging benefit is not a black box.
| Tenor (y) | Sensitivity | Risk weight | Weighted | Share of gross |
|---|---|---|---|---|
| 1 | $120,000 | 1.70% | $2,040 | 24.3% |
| 2 | -$60,000 | 2.00% | -$1,200 | 14.3% |
| 5 | -$80,000 | 2.60% | -$2,080 | 24.8% |
| 10 | $45,000 | 3.60% | $1,620 | 19.3% |
| 30 | -$30,000 | 4.80% | -$1,440 | 17.2% |
Build-up: delta $1,658 + vega $20,000 + curvature $25,000 + default risk $6,000,000 + residual $240,000 + securitisation $0.00 = $6,286,658. Tenor weights follow the published ladder (1y 1.70%, 30y 4.80%).
WS_k = RW_k · s_k · Sign preserved: it drives the netting.
ρ_kl = max(e^{−θ|T_k−T_l|/min(T_k,T_l)}, 0.40) · θ = 3% for GIRR.
K = √(Σ WS² + Σ_{k≠l} ρ WS_k WS_l) · One currency bucket, so no cross-bucket term.
Σ|WS| − K · What the correlations give back.
A clear path from inputs to results.
The standardised approach does not net positions by magic: it weights each tenor sensitivity, correlates the tenors, and aggregates. This is the general interest rate risk delta charge for one currency bucket, with the correlation matrix visible so the hedging benefit is not a black box.
How to use
- Enter one sensitivity per tenor: the value change for a one basis point move.
- Set the supervisory risk weight for each tenor.
- Adjust the correlation decay and the floor.
- Read the capital charge, the gross charge and the hedging benefit.
- Check the correlation matrix to see which pairs are actually diversifying.
The formula
Reference: BCBS MAR21 (FRTB standardised approach), general interest rate risk delta charge, intra-bucket aggregation.
Worked example
Five tenors, mixed signs, one currency
- Sensitivities: +120k at 1y, −60k at 2y, −80k at 5y, +45k at 10y, −30k at 30y.
- Risk weights 1.7%, 2.0%, 2.6%, 3.6% and 4.8%.
- Correlation decay θ = 3%, floor 40%.
- 1
Weighted sensitivities: +2,040, −1,200, −2,080, +1,620, −1,440.
- 2
The absolute sum is 8,380 — the charge if nothing netted.
- 3
The 1y and 2y pair correlate at 0.97, so they nearly cancel; the 1y and 30y pair only at 0.42.
- 4
Aggregating with the correlation matrix gives a charge of 1,658.
- 5
The hedging benefit is 6,722, so the charge is 20% of the gross.
Charge 1,658 · gross 8,380 · 80% of the gross removed by netting.
Interpreting the result
The correlation floor is what stops a 1-year and a 30-year position from being treated as a free hedge. Without it, a steepener and a flattener at opposite ends of the curve would net to almost nothing; with it, the charge keeps a residual that reflects the risk the curve does not move in parallel.
Assumptions & limitations
- One currency bucket, delta only: no vega, no curvature, no cross-bucket aggregation.
- Tenor weights follow the published ladder, interpolated between the anchor tenors; confirm the table against the current MAR21 text before reporting.
- The residual risk add-on is 1% of exotic notional and 0.1% of other notional.
- Sensitivities are already scaled to a one basis point move.
- No default risk charge and no residual risk add-on.
Frequently asked questions
Why is the floor 40%?
Because beyond a certain tenor gap the empirical correlation stops falling. The floor keeps a long-dated hedge worth something, which is both prudent and closer to how curves actually move.
Is this the whole FRTB charge?
No. It is the GIRR delta component. A full charge adds vega and curvature, the other risk classes, cross-bucket aggregation and the default risk charge.
What is θ?
The decay rate of the correlation with the tenor gap. GIRR uses 3%, so a 1-year and a 2-year position correlate at about 0.97 while a 1-year and a 30-year position sit near the floor.
Why do the risk weights matter so much?
They set the scale of every weighted sensitivity. A 10% error in the ladder is a 10% error in the charge, which is why they are inputs rather than hard-coded.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.