The standardised approach for counterparty credit risk in one netting set, from supervisory duration to the multiplier, and why netting cuts the exposure by more than half.
Under the standardised approach for counterparty credit risk (SA-CCR), the exposure at default of a netting set is EAD = 1.4 × (replacement cost + multiplier × aggregate add-on). For an illustrative unmargined netting set of two euro swaps and two EUR/USD forwards worth 1.2 million net, the interest rate add-on is 1.88 million, the FX add-on 0.76 million and the exposure at default 5.38 million. Booked trade by trade without netting, the same four trades would carry 13.10 million.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
SA-CCR replaced the current exposure method in the EU from June 2021 and is the default way a bank measures derivative exposure for credit risk capital. The same machinery, with its own adjustments, feeds the leverage ratio exposure and the large exposures test, so a desk that adds an offsetting trade or a collateral agreement moves three ratios at once. The formula has five moving parts. Each is simple; the order matters.
| Trade | Notional | Residual maturity, years | Delta | Market value |
|---|---|---|---|---|
| Pay-fixed swap, 4 years | 100.0 | 4 | +1 | 3.0 |
| Receive-fixed swap, 8 years | 80.0 | 8 | −1 | −2.1 |
| Buy USD forward, 6 months | 55.0 | 0.5 | +1 | 0.5 |
| Sell USD forward, 1 year | 20.0 | 1 | −1 | −0.2 |
| Netting set | 255.0 | 1.2 |
Delta is +1 for a trade that gains when its primary risk factor rises: a pay-fixed swap gains when rates rise, a long USD forward gains when the dollar rises. The FX notionals are the foreign currency leg converted to euros. No collateral is held.
EAD = α × (RC + PFE), α = 1.4
RC = max(V − C, 0); PFE = multiplier × (AddOnIR + AddOnFX)
Multiplier = min{1; 0.05 + 0.95 × exp[(V − C) ÷ (2 × 0.95 × AddOn)]}
Supervisory duration for rates: =(EXP(-0.05*S)-EXP(-0.05*E))/0.05. Maturity factor, unmargined: =SQRT(MIN(M,1)).
Step 1: replacement cost. The netting set is worth 1.2 million to the bank and no collateral is held, so RC = 1.2.
Step 2: the interest rate add-on. Each swap notional is multiplied by its supervisory duration. The 4-year swap: 100.0 × 3.6254 = 362.54. The 8-year swap: 80.0 × 6.5936 = 527.49. Both mature beyond a year, so their maturity factor is 1. The 4-year swap sits in the 1 to 5 year bucket with a positive sign, the 8-year swap in the over 5 year bucket with a negative sign. The buckets are combined with a partial offset:
Effective notional = √(D1² + D2² + D3² + 1.4 D1D2 + 1.4 D2D3 + 0.6 D1D3)
Here D1 = 0, D2 = 362.54 and D3 = −527.49: √(131,434 + 278,244 − 267,729) = √141,949 = 376.76. At the 0.5 per cent supervisory factor, the add-on is 1.88.
Step 3: the FX add-on. Both forwards are in the EUR/USD hedging set, where long and short positions offset in full. The 6-month forward has a maturity factor of √0.5 = 0.7071, so it counts as 38.89; the 1-year forward counts as −20.00. Net, 18.89, times the 4 per cent supervisory factor: 0.76.
Step 4: the multiplier and the PFE. The aggregate add-on is 2.64. Because the netting set has a positive value, the multiplier is 1.0000 and the PFE equals the add-on, 2.64.
Step 5: exposure at default. 1.4 × (1.2 + 2.64) = 5.38 million.
On 255.0 million of gross notional the exposure at default is 5.38 million, 2.11 per cent. At a 100 per cent counterparty risk weight that is 5.38 million of risk-weighted assets and 0.43 million of capital at the 8 per cent minimum, before any credit valuation adjustment charge, which is calculated separately.
The offset inside the rates hedging set does most of the work. With no offset at all between the two swaps, adding their effective notionals in absolute value, the add-on would be 4.45 instead of 1.88: the bucket formula saves 2.57 million of add-on because the bank pays fixed on one swap and receives fixed on the other, even though their maturities differ.
| Variant | Net value less collateral | Multiplier | EAD |
|---|---|---|---|
| Base case, one netting set | 1.2 | 1.0000 | 5.38 |
| Each trade in its own netting set | 13.10 | ||
| Net value of −1.5, no collateral | −1.5 | 0.7544 | 2.79 |
| Net value of 1.2, 3.0 of collateral held | −1.8 | 0.7135 | 2.64 |
Without a netting agreement the four trades sum to 13.10 million, 2.44 times the netted figure: the 4-year swap alone is 6.74 and the 6-month forward 2.88. The value of a netting opinion for a counterparty is visible in that one line. When the netting set is out of the money, replacement cost falls to zero and the multiplier drops below 1, recognising that the bank would have to gain a lot before it is exposed again. Collateral held works the same way through V − C.
Compute SA-CCR in order: replacement cost, add-ons by hedging set with their signs, the multiplier, then 1.4 times the total. On this netting set that is 5.38 million, less than half of the unnetted figure. Derivative exposure is one of the inputs that decide which of a bank's constraints actually binds, and the free workbooks for this case run every ratio from the same balance sheet. The large exposure limit shows where the same counterparty exposure lands next.
Alpha is a fixed supervisory multiplier of 1.4 applied to the sum of replacement cost and potential future exposure. It was carried over from the internal model method, where it covers the gap between expected positive exposure and a stressed, concentrated portfolio. On the illustrative netting set it turns 3.84 million of replacement cost and PFE into an exposure at default of 5.38 million.
Through two channels. Replacement cost floors at zero, and the multiplier falls below 1 when the netting set is out of the money, down to a floor of 5 per cent. In the illustrative case a net value of minus 1.5 million gives a multiplier of 0.7544, a PFE of 1.99 and an EAD of 2.79 million, about half the 5.38 million at a positive value of 1.2.
For interest rate and credit trades the adjusted notional is the notional times a supervisory duration, (exp(-0.05 x S) - exp(-0.05 x E)) / 0.05, with S and E the start and end dates in years. For a swap that has started and ends in 4 years it is 3.6254, so 100.0 million of notional counts as 362.54 before the 0.5 per cent supervisory factor is applied.
This article is one calculation from Financial Regulation. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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