CVA capital: the basic approach

RiskAtoms Bank plc's four derivative counterparties have not missed a payment, and three of them post collateral. Yet the bank must hold £3.89m of capital against them on top of the counterparty credit risk capital for default: £48.6m of RWA. That is the charge for CVA riskCVA risk: the risk of losses from changes in CVA caused by changes in counterparty credit spreads and in the market risk factors that drive exposure (MAR50.4)., the risk that the price of their default risk rises. This lesson takes the £48.6m from L4.1.04: Risk-weighted assets apart, and shows what a CDS hedge would do to it.

What is being capitalised

L3.4.10: CVA basics priced counterparty risk as CVA and showed that it moves every day with the counterparty's credit spread. In the 2007–09 crisis about two-thirds of banks' counterparty losses came from those moves rather than from defaults. Default is covered by counterparty credit risk capital (M4.4: Counterparty, operational and large exposures). CVA capital covers the mark-to-market losses before any default. The rules work with regulatory CVARegulatory CVA: CVA as the capital rules define it, which ignores the bank's own default (no DVA) and must meet extra conditions (MAR50.3)., which leaves out the bank's own default (MAR50.3), so there is no DVA in it.

The charge applies to covered transactionsCovered transactions: the trades that count for CVA capital: all derivatives except those with a qualifying central counterparty, and fair-valued SFTs if the supervisor finds them material (MAR50.5).: every derivative except those with a qualifying central counterparty, and securities financing transactions only if the supervisor deems their CVA risk material (MAR50.5). The trading desk's cleared futures, swap and forward are out; the four bilateral netting sets of M3.4: Counterparty credit risk are in. Banks use the basic approach, BA-CVA, unless the supervisor approves the standardised one, SA-CVA (MAR50.7; L4.3.10: CVA capital: the standardised approach).

A bank whose non-centrally cleared derivatives total €100bn or less may skip both and set CVA capital equal to 100% of its counterparty credit risk capital (MAR50.9). RiskAtoms Bank plc has £1,430m, far below the thresholdMateriality threshold: €100bn of non-centrally cleared derivatives notional. A bank at or below it may set CVA capital to 100% of its counterparty credit risk capital (MAR50.9)., so it could use £31.2m of RWA instead of £48.6m. The option covers the whole portfolio, recognises no hedges, and the supervisor can withdraw it. Module 4.1 used BA-CVA, and so does this lesson.

One counterparty at a time

BA-CVA does not compute CVA. It builds a proxy for how far each counterparty's CVA could move, the stand-alone CVA capitalStand-alone CVA capital S_c: RW × M × EAD × DF ÷ α for one counterparty, the BA-CVA's proxy for how much its CVA could move. $S_c$: a supervisory risk weight for the counterparty's sector and credit quality (MAR50.16, Table 1), times the netting set's effective maturity, its EAD from SA-CCR and a discount factor. Three details matter:

• The discount factor $(1-e^{-0.05M})/(0.05M)$ is the average over the life of the netting set of a continuously compounded discount factor at 5% (M-A05: The number e and continuous growth). For EBB's ten-year swap it is 0.7869.
• The EAD already contains SA-CCR's α of 1.4. BA-CVA divides it out, because α turns expected exposure into EAD (MAR50.14, footnote 4).
• M is not capped at five years, as it would be for IRB (MAR50.15): EBB counts at its full ten.

EBB, a pension fund, has no row of its own in Table 1; Module 4.1 files it under financials, and treats its internal AA rating as investment grade, which MAR50.16 allows only if the supervisor approves the mapping (otherwise the not-rated weight applies). SAL, a hedge fund with no rating, takes the high-yield and not-rated weight.

Adding them up: ρ = 50%

The four figures cannot simply be added. Spreads move partly together, with the economy, and partly on their own. BA-CVA splits K into a systematic part and an idiosyncratic part with a supervisory correlation ρ = 50% (MAR50.14). If the four moved in lockstep, K would be the sum, 8.078; if they were independent, the square root of the sum of squares, 5.091. The formula gives 5.979, with 46% of K² systematic. Written out, it is the quadratic form of M-E02: Matrix multiplication and quadratic forms with a correlation of ρ² = 25% between any two counterparties' CVA (M-C10: Covariance and correlation). Then the discount scalarDiscount scalar DS: 0.65, a fixed multiplier on BA-CVA capital that calibrates the basic approach to the standardised one. of 0.65: capital £3.886m, RWA £48.58m.

Hedges: the full version

Only hedges bought to reduce the counterparty credit spread part of CVA, and managed that way, count (MAR50.17). Under BA-CVA that means single-name CDS, single-name contingent CDS and index CDS (MAR50.18). They leave the market risk charge: eligible external CVA hedges are excluded from market risk capital (MAR50.11). The full version then needs three pieces:

• SNHSNH_c: the single-name hedges of counterparty c, each weighted by r_hc, its correlation with the counterparty's spread.: a single-name CDS reduces its counterparty's S_c by r_hc × RW × M × notional × DF, where r_hc is 100% for the counterparty itself, 80% for a legally related name and 50% for a name in the same sector and region (MAR50.26).
• IHIH: the index hedges, which reduce only the systematic part of K.: an index CDS offsets only the systematic part, with its risk weight scaled by 0.7 for diversification (MAR50.24).
• HMAHMA_c: hedge misalignment, the part of an imperfect single-name hedge (r_hc below 100%) that adds back to K.: an imperfect single-name hedge adds back (1 − r_hc²) of its term, squared.

The result, K_hedged, is blended with K_reduced: ββ: 0.25 in the full BA-CVA, the share of the unhedged figure that stays however much is hedged (MAR50.20). = 25% of the unhedged K always stays (MAR50.20). That is the price of a crude model. However well hedged, this bank's CVA capital cannot fall below £0.972m (£12.15m of RWA). The bank chooses between the full and reduced versions, but every BA-CVA bank must calculate the reduced one (MAR50.13).

BA-CVA in full (MAR50.14–50.26; the formulas are images on bis.org and were read as text in the PRA Rulebook, Credit Valuation Adjustment Risk Part, rules 4.2–4.10):

• $\text{RW}_c$: Table 1 weight, 0.5% to 5% for investment grade and 2% to 12% for high yield or not rated (MAR50.16). $M_{NS}$: the netting set's effective maturity, uncapped. $\text{EAD}_{NS}$: as for counterparty credit risk capital. α = 1.4. DF = 1 for a bank using the internal model method.
• ρ = 50%; β = 0.25; DS = 0.65. $B_h$, $M_h$: a hedge's notional and remaining maturity. $r_{hc}$: 100%, 80% or 50% (Table 2). Index weights × 0.7.
• $K_{\text{reduced}}^2 = \sum_i\sum_j c_{ij} S_i S_j$ with $c_{ii} = 1$ and $c_{ij} = \rho^2$: expand $(\rho\sum S)^2$ and the ρ² on the diagonal cancels with $(1-\rho^2)$.

Start with £5m of CDS on Corriemoor. Add index protection: K falls until IH reaches ρ Σ(S − SNH), about £22.5m, and rises again beyond it. Then switch the CDS reference to a sector-and-region proxy and watch most of its benefit go: less is netted, so the best index size moves up to about £24.3m. Finally switch Ebbsworth to the UK weight.

£ millions. EAD and M from Module 4.1 (SA-CCR); risk weights from MAR50.16.

Basel: MAR50, in force since 1 January 2023 in the Basel Framework, after the Committee recalibrated both approaches in July 2020. Jurisdictions as at 3 November 2026 as at 3 Nov 2026.

• CVA capital covers mark-to-market losses from counterparty spreads, before any default; regulatory CVA has no DVA (MAR50.3–50.5).
• S_c = RW × M × EAD × DF ÷ 1.4 per counterparty; K_reduced combines them with ρ = 50%; capital is 0.65 × K. The bank: K 5.979, capital £3.89m, RWA £48.6m.
• Only single-name, contingent and index CDS count, through SNH, IH and HMA; β = 25% keeps a quarter of K. A £5m CDS on COR gives £45.8m; adding £10m of index £40.8m.
• At or below €100bn of non-cleared notional a bank may use 100% of CCR capital instead: £31.2m here, with no hedge recognition.
• The UK weights pension funds at 3.5% (RWA £38.4m) and removes the old exemptions with a legacy option to 2030; the EU keeps them.

CVA risk

CVA risk: the risk of losses from changes in CVA caused by changes in counterparty credit spreads and in the market risk factors that drive exposure (MAR50.4).

Regulatory CVA

Regulatory CVA: CVA as the capital rules define it, which ignores the bank's own default (no DVA) and must meet extra conditions (MAR50.3).

Covered transactions

Covered transactions: the trades that count for CVA capital: all derivatives except those with a qualifying central counterparty, and fair-valued SFTs if the supervisor finds them material (MAR50.5).

Stand-alone CVA capital (S_c)

Stand-alone CVA capital S_c: RW × M × EAD × DF ÷ α for one counterparty, the BA-CVA's proxy for how much its CVA could move.

Discount scalar (DS)

Discount scalar DS: 0.65, a fixed multiplier on BA-CVA capital that calibrates the basic approach to the standardised one.

β (BA-CVA full)

β: 0.25 in the full BA-CVA, the share of the unhedged figure that stays however much is hedged (MAR50.20).

SNH

SNH_c: the single-name hedges of counterparty c, each weighted by r_hc, its correlation with the counterparty's spread.

IH

IH: the index hedges, which reduce only the systematic part of K.

HMA

HMA_c: hedge misalignment, the part of an imperfect single-name hedge (r_hc below 100%) that adds back to K.

Materiality threshold

Materiality threshold: €100bn of non-centrally cleared derivatives notional. A bank at or below it may set CVA capital to 100% of its counterparty credit risk capital (MAR50.9).