CVA capital: the standardised approach · RiskAtoms Academy

By the end you will be able to

1Compute regulatory CVA from survival and marginal default probabilities implied by credit spreads.
2Explain CVA sensitivities to counterparty spreads by tenor and to interest rates, and why some are negative.
3Aggregate weighted sensitivities into SA-CVA capital with buckets, correlations and the hedging disallowance.
4Compare SA-CVA with BA-CVA on the same book and say what the approach demands of a bank.

Why it matters

Under the basic approach RiskAtoms Bank plc's CVA RWA are £48.6m. Run the standardised approach on the same four netting sets and they come out at £24.3m illustrative. SA-CVA starts from the bank's own CVA model: it sees the collateral, the real spreads and every hedge. The price is permission, a CVA desk and a monthly run of sensitivities, which a bank with four derivative counterparties would not pay.

Core explanation

Capital from the CVA model itself

Illustrative dataRiskAtoms Bank plc's capital book

The same made-up UK bank as Level 3: £67bn of assets and £4bn of equity at 31 December 2025, in £ millions. Module 4.1 adds its regulatory layer: own funds, deductions, risk-weighted assets by risk type, buffers, the leverage exposure and MREL, computed from the Level 3 credit, trading, derivatives and operational risk books. Every figure is illustrative, not any bank's data.

Pro forma. The book applies Basel 3.1, the 2017 finalisation of Basel III, to the 31 December 2025 balance sheet. On that date the bank still reported under the old UK CRR. The UK applies Basel 3.1 from 1 January 2027, and the internal model approach for market risk from 1 January 2028 (PRA PS1/26, paras 1.23 and 1.24). So the book shows the bank as it would look under the new rules.

The CVA data. The four netting sets of the Level 3 derivatives book (Module 3.4): Halvergate Moor Manufacturing (HAL), Corriemoor Bank (COR), Saltney Capital (SAL) and Ebbsworth Pension Trustees (EBB), all invented. Module 4.1 gave each its SA-CCR exposure and maturity, and set CVA RWA at £48.6m with the reduced basic approach. The bank has no CVA hedges; any hedge on these pages is added for illustration.

Illustrative. SA-CVA needs the supervisor's approval and a CVA desk (MAR50.7, MAR50.30). RiskAtoms Bank plc has neither, so every SA-CVA figure here shows what the approach would give, not what the bank reports.

Start from regulatory CVA

SA-CVA adapts the market risk standardised approach of L4.3.02: The sensitivities-based method: delta and vega to CVA, with fewer risk factors and no default or curvature charge (MAR50.27). Its inputs are sensitivities of regulatory CVA, so the bank must first compute it for every counterparty (MAR50.31). The principles are in MAR50.32: exposure paths from the bank's simulation, discounted; default probabilities implied by the counterparty's credit spreads, with proxy spreads from liquid peers where there is no market; and one market LGD used both to read the PDs and to compute the loss.

L3.3.16: Market-implied default risk read default intensities from spreads, and L3.4.10: CVA basics priced CVA with them. MAR50.32(2)–(3) asks only for a term structure of PDs estimated from credit spreads; the formula is written out in the Basel III text of June 2011 (para 98) and in the old UK CRR Article 383(1), with a survival probability $S(t) = e^{-s(t)\,t/\text{LGD}}$ and a marginal default probability for each period, the fall in survival across it (M-C14: Survival and marginal default probabilities). Halvergate Moor has no traded CDS, so its 180bp is a proxy spread from peers, as MAR50.32 allows. At that spread and LGD 60%, the intensity is 3.0% a year: survival to five years is 86.07%, and the chance of defaulting in year five is 2.62%.

Year	Survival at end	Marginal PD	EE mid-year	DF mid-year	CVA in the year
1	97.04%	2.96%	2.246	0.9806	0.0373
2	94.18%	2.87%	2.470	0.9429	0.0397
3	91.39%	2.78%	2.653	0.9066	0.0401
4	88.69%	2.70%	2.557	0.8717	0.0358
5	86.07%	2.62%	2.174	0.8382	0.0283
6	83.53%	2.54%	1.631	0.8060	0.0197
7	81.06%	2.47%	0.891	0.7750	0.0098
8	78.66%	2.40%	0.000	0.7452	0.0000
9	76.34%	2.32%	0.000	0.7165	0.0000
10	74.08%	2.26%	0.000	0.6889	0.0000
Total					0.2107

£m. The CVA column is each year's share of the exact sum on the simulation's 24 steps a year (EE and PD per step), so it is £211k as in L3.4.10: CVA basics. HAL has no CSA; its swap ends in year 7.

From CVA to sensitivities

Capital is then built from how CVA moves. A sensitivity is a partial derivative (M-B02: Partial derivatives): bump one factor by 1bp, hold the rest, divide the change by 0.0001. For the counterparty credit spread the factors are the spread at five tenors, 0.5, 1, 3, 5 and 10 years, for each name (MAR50.65). For interest rates they are the risk-free rate at 1, 2, 5, 10 and 30 years in each major currency (MAR50.56). There are six risk classes in all (interest rate, FX, counterparty credit spread, reference credit spread, equity, commodity), each with a delta charge, and vega for all but the counterparty spread.

CVA sensitivity to each tenor of the counterparty's spread, £ per bp; regulatory CVA under the CSA where there is one
Set	Bucket, quality	0.5y	1y	3y	5y	10y	CS01
HAL	3, IG (RW 3%)	−56	19	123	770	213	1,069
COR	2, IG (RW 5%)	0	−17	181	189	368	721
SAL	2, HY (RW 12%)	−7	64	76	0	0	132
EBB	2, IG (RW 5%)	−32	6	71	569	2,490	3,105

The tenor sensitivities add up, to second order, to the parallel CS01 of L3.4.10: CVA basics. Some are negative. Bumping HAL's 0.5-year node with the 1-year node fixed leaves survival to one year unchanged and only brings defaults forward into the first months, when the swap's exposure is still small, so CVA falls. EBB's CVA sits almost all at ten years, where its swap's exposure lives.

Weights, buckets and correlations

Each sensitivity is multiplied by a supervisory risk weight, set by bucket (sector) and quality: 3% for investment-grade industrials (bucket 3), 5% or 12% for financials (bucket 2), with no difference by tenor (MAR50.65, Table 7). Within a bucket, two factors correlate at the product of three parts: 90% if the tenors differ, 50% if the names differ (90% if legally related), 80% if one is investment grade and the other not. Across buckets a γ applies: 5% between financials and industrials (Table 6). The algebra is the quadratic form of M-E02: Matrix multiplication and quadratic forms, as in the market risk charge. Hedges enter as negative sensitivities on the same factors, and the hedging disallowance R keeps 1% of their squared size.

ExploreHow SA-CVA is built

Click a box to see what happens there.

Regulatory CVA

Exposure simulation, market-implied PDs, market LGD, per counterparty. No DVA. Must be calculated at least monthly (MAR50.30).

What it takes

Banks use BA-CVA unless the supervisor approves SA-CVA (MAR50.7). To qualify a bank must be able to model exposure and compute CVA and its sensitivities at least monthly, and must have a CVA desk or similar function that manages and hedges CVA (MAR50.30). Netting sets it cannot model can be carved out to BA-CVA (MAR50.8). SA-CVA is calculated and reported monthly, like the market risk standardised approach (MAR50.28). For a bank with four derivative counterparties, that is a large machine for a small charge, which is why RiskAtoms Bank plc stays on BA-CVA.

The formal version

Regulatory CVA, in the form written out in Basel III (June 2011, para 98) and the old UK CRR Article 383(1) (MAR50.32(1)–(3) states only the principles: expected loss from counterparty default, from market-implied PDs, a market LGD and simulated discounted exposure), then the SA-CVA aggregation (MAR50.47–50.53; the K_b and K formulas are images on bis.org; see the review notes for the copies read):

\begin{aligned} S(t) &= e^{-s(t)\,t\,/\,\text{LGD}_{\text{MKT}}}, \qquad \text{PD}(t_{i-1}, t_i) = \max\big(S(t_{i-1}) - S(t_i),\ 0\big) \\ \text{CVA} &= \text{LGD}_{\text{MKT}} \sum_{i=1}^{n} \text{EE}(t_i)\,\text{DF}(t_i)\,\text{PD}(t_{i-1}, t_i) \\ s_k &= \frac{\text{CVA}(x_k + 0.0001) - \text{CVA}(x_k)}{0.0001}, \qquad \text{WS}_k = \text{RW}_k\big(s_k^{\text{CVA}} - s_k^{\text{Hdg}}\big) \\ K_b &= \sqrt{\sum_{k \in b} \text{WS}_k^2 + \sum_{k \in b}\sum_{l \in b,\, l \neq k} \rho_{kl}\,\text{WS}_k\,\text{WS}_l + R \sum_{k \in b} \big(\text{WS}_k^{\text{Hdg}}\big)^2} \\ S_b &= \max\Big(-K_b,\ \min\Big(\sum_{k \in b} \text{WS}_k,\ K_b\Big)\Big) \\ K &= m_{\text{CVA}} \sqrt{\sum_b K_b^2 + \sum_b \sum_{c \neq b} \gamma_{bc}\,S_b\,S_c}, \qquad \text{Capital} = \sum_{\text{classes}} K \end{aligned}

$s(t)$ : the credit spread for maturity t, linear between the tenors. $\text{EE}(t_i)$ : expected exposure under the margin agreement; $\text{DF}$ : risk-free discount factor. Article 383 averages EE × DF across each period; this book takes the end of each step.
Counterparty credit spread: $\rho_{kl} = \rho_{\text{tenor}}\,\rho_{\text{name}}\,\rho_{\text{quality}}$ with 90%, 90% or 50%, and 80% (MAR50.65). Interest rate: tenor correlations from 91% to 31% (Table 4), weights 1.11% at 1 year down to 0.74% from 5 years (Table 3).
R = 0.01; $m_{\text{CVA}} = 1$ (MAR50.41); RWA = 12.5 × capital.

Try it

Buy ten-year protection on Ebbsworth and push the notional up: K falls, bottoms out at £4.40m (RWA £8.19m), then rises as the hedge overshoots. Switch to five years and the hedge sits on the wrong tenor. Then try Corriemoor: a CDS on one financial also hedges the other two, through the name correlation: 50% for Ebbsworth, but 50% × 80% = 40% for SAL, which is high yield.

Try itHedge a counterparty under SA-CVA

Buy CDS protection on

CDS maturity

Notional (£m)£0.00m

Tenor	WS of EBB's CVA	Net
0.5y	−0.0159	−0.0159
1y	0.0032	0.0032
3y	0.0355	0.0355
5y	0.2846	0.2846
10y	1.2452	1.2452

Bucket	K_b	S_b	R × Σ WS_hdg²
3 Industrials (HAL)	0.3138	0.3138	0.00000
2 Financials (COR, SAL, EBB)	1.7969	1.7969	0.00000

Hedge CS01 (£ per bp) vs EBB's0 vs 3,105

Credit spread delta K1.8395

Interest rate delta K0.1039

SA-CVA capital (illustrative)£1.943m

SA-CVA RWA (illustrative)£24.29m

Reduced BA-CVA RWA£48.58m

R = 0.01: 1% of each squared hedge sensitivity stays in K_b.

No hedge: this is the bank's illustrative SA-CVA.

Simplification: the hedge's whole sensitivity is put on its maturity tenor (notional × risky annuity at the counterparty's spread, quarterly premiums). A full calculation bumps every tenor.

Worked example

SA-CVA on the four netting sets (illustrative)

£ millions. Regulatory CVA uses m3-4's simulated EE (2,000 paths), under the CSA for COR, SAL and EBB; flat spreads at the m3-4 CDS levels; LGD 60%.

From CVA to capital

Step 1 of 6

1
Regulatory CVA
HAL 0.211, COR 0.053, SAL 0.035, EBB 0.128: 0.426 in all. The CSAs keep COR, SAL and EBB small; uncollateralised HAL is half the total.

Against reduced BA-CVA (capital £3.886m, RWA £48.58m), SA-CVA is half. The comparison flatters it. Three of the four sets are collateralised, which SA-CVA sees through the EE and BA-CVA only partly through the EAD. And this run leaves out FX delta (HAL's dollar forward), equity delta (SAL's index put) and every vega, each of which would add to the total.

Hedging under SA-CVA

Regulatory lens

Basel: MAR50.27–50.77, in force since 1 January 2023. Jurisdictions as at 3 November 2026 as at 3 Nov 2026.

In the UK

SA-CVA is in Chapter 5 of the PRA's Credit Valuation Adjustment Risk Part from 1 January 2027 (PS1/26, para 1.23), with permission. The PRA kept the margin period of risk floor for the exposure model, allows proxy spreads where no spread data exist, and splits financial counterparties into two categories (PS17/23, chapter 4). The parts of Chapter 5 read for this lesson follow Basel; the bucket formula was not in the text read.

In the EU

CRR3 has applied the standardised approach for CVA risk since 1 January 2025, with the competent authority's permission (Article 382a(1)(a)), alongside the basic and simplified approaches.

In the US

The 19 March 2026 proposal includes a risk-sensitive CVA framework for large and trading-heavy firms; as far as we could find, it was not final by 3 November 2026 (L4.3.11: Market risk and CVA capital: what changes from 2027).

Spark Atoms

Spark AtomVega without options

A plain interest rate swap has no volatility in its price, but its CVA does: the exposure simulation draws rate paths with a volatility. So SA-CVA treats vega as always material and requires it even for a book with no options, shifting the volatilities used to generate the paths (MAR50.48).

Spark AtomOne LGD, twice

The market LGD appears inside the survival probability and outside the sum. Raise it, and the PDs implied by a given spread fall while the loss on default rises: the two nearly cancel. That is why MAR50.32(4) requires the same value in both places.

Key takeaways

Regulatory CVA uses market-implied survival S(t) = e^(−s t / LGD), marginal PDs S(t_{i−1}) − S(t_i), simulated EE under the CSA, and one market LGD (MAR50.32; formula as in Basel III 2011 para 98 and old CRR Art 383(1)).
SA-CVA capital comes from CVA sensitivities: counterparty spread at 0.5 to 10 years, rates at 1 to 30 years, and four other classes, delta and vega (none for counterparty spread).
Weighted sensitivities aggregate within buckets (with R = 1% on hedges) and across buckets with γ; m_CVA = 1; risk classes add.
Illustrative on the bank: credit spread 1.839 + interest rate 0.104 = £1.94m, RWA £24.3m, against BA-CVA's £48.6m; omitted FX, equity and vega would add to it.
SA-CVA needs approval, monthly CVA and sensitivities, and a CVA desk (MAR50.7, 50.30): the bank uses BA-CVA.

Reaction

Check what stuck

Glossary

Survival probability: Survival probability S(t): the chance the counterparty has not defaulted by time t. From a credit spread s and market LGD, S(t) = e^(−s t / LGD).
Marginal default probability: Marginal default probability: the chance of default within one period, S(t_{i−1}) − S(t_i), as opposed to the cumulative probability of default by t.
Market LGD (ELGD): Market LGD (ELGD): the loss given default that market participants price into credit spreads, used both to read PDs from spreads and to compute CVA (MAR50.32).
Sensitivity: Sensitivity s_k: the change in CVA (or a hedge's value) when one risk factor moves by a small amount, divided by that amount. For spreads and rates, 1bp ÷ 0.0001.
Bucket: Bucket: a group of risk factors aggregated together. For counterparty credit spread, a sector (Table 5); for interest rates, a currency.
Hedging disallowance R: Hedging disallowance R: 0.01. A share of each squared hedge sensitivity that stays in K_b, so that a hedge never offsets CVA perfectly (MAR50.53).
m_CVA: m_CVA: a multiplier on SA-CVA capital, set at 1; the supervisor can raise it if the bank's CVA model risk is too high (MAR50.41).
CVA desk: CVA desk: the team, or a similar dedicated function, responsible for managing and hedging CVA risk. SA-CVA requires one (MAR50.30).

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, MAR50, paras 50.27–50.77: the full SA-CVA, including the FX, reference credit, equity and commodity classes not computed here. Advanced.
M6.5: Counterparty risk and XVA: exposure simulation, CVA sensitivities and hedging on an XVA desk. Advanced.

Origins

Basel Committee on Banking Supervision, MAR50: Credit valuation adjustment framework, paras 50.7, 50.8, 50.27–50.65, version effective 1 January 2023, bis.org; and the Swiss SIF copy.
Saudi Central Bank (SAMA) Rulebook, the Basel CVA framework as adopted, paras 11.51–11.65 (the bucket aggregation in words, the hedge sign convention and the correlation parts).
Regulation (EU) No 575/2013 as it applies in the UK, Article 383(1) (the old advanced CVA method), legislation.gov.uk.
Basel Committee on Banking Supervision, Basel III: A global regulatory framework for more resilient banks and banking systems, revised version June 2011, para 98, bis.org.
Prudential Regulation Authority, PRA Rulebook: Credit Valuation Adjustment Risk Part, from 1 January 2027; PS17/23, December 2023, chapter 4; PS1/26, 20 January 2026, para 1.23.
Regulation (EU) No 575/2013 (CRR), Article 382a, as amended by Regulation (EU) 2024/1623.

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