Do CVA hedges reduce capital under BA-CVA?

Under the reduced version, no. Under the full version, only single-name CDS, single-name contingent CDS and index CDS on the counterparty spread count (MAR50.18), and the benefit is floored: a quarter of the unhedged charge always remains (MAR50.20).

What happens to a CVA hedge that is not eligible?

It is treated as a trading-book instrument and carries market-risk capital (MAR50.11(3)), so it adds capital rather than reducing it.

Which hedges count under SA-CVA?

Instruments that hedge the counterparty credit spread and instruments that hedge the exposure component of CVA (MAR50.38), as whole transactions managed as CVA hedges (MAR50.37). Tranched credit derivatives are not eligible (MAR50.39).

Why do some banks not hedge CVA?

On the reduced basic approach no hedge reduces the CVA charge and every hedge adds market-risk capital, so hedging raises total capital. Such banks carry CVA volatility in profit and loss instead.

Can a hedge reduce SA-CVA capital to zero?

No. A hedging disallowance parameter, R = 0.01, prevents perfect offset (MAR50.53).

Explainer

CVA hedges and capital: which hedges count under BA-CVA and SA-CVA

A CVA hedge can steady P&L and still raise capital. Which hedges the rules recognise under each approach, what happens to the ones they do not, and why the choice of approach decides whether hedging CVA pays.

The short answer

A CVA hedge does two jobs that the rules keep apart. In the accounts, CVA is part of the fair value of the derivatives book, so a hedge that moves against CVA steadies profit and loss. In regulatory capital, a hedge reduces the CVA charge only if the approach the bank uses recognises it; a hedge that is not recognised is treated as an ordinary trading position and needs market-risk capital of its own. Under the reduced basic approach no hedge is recognised, so hedging CVA adds capital. Under the full basic approach only credit default swaps on the counterparty spread count. Under the standardised approach both credit-spread and exposure hedges count. Which approach a bank uses therefore decides whether hedging CVA saves capital or costs it.

What a CVA hedge hedges

CVA moves for two reasons:

the counterparty’s credit: if its credit spread widens, the expected loss from its default rises, and CVA rises;
the exposure: if markets move so the counterparty owes the bank more (rates, FX, equity, commodities), there is more to lose, and CVA rises.

Hedges follow the same split. Credit-spread hedges are credit default swaps (CDS) on the counterparty, on a related name, or on an index. Exposure hedges are rate, FX, equity or commodity trades that gain when the exposure grows.

Where a hedge that does not count ends up

The rules decide first whether a hedge is an eligible CVA hedge under the approach the bank uses (MAR50.10). Then:

eligible external hedges come out of the market-risk calculation and reduce the CVA charge (MAR50.11(2));
ineligible external hedges are trading-book instruments and carry market-risk capital like any other position (MAR50.11(3));
internal hedges, a trade between the CVA desk and a trading desk, count only if eligible; if not, both legs sit in the trading book and cancel out (MAR50.11(4)).

A hedge the CVA approach does not recognise is therefore not neutral. It leaves the CVA charge where it was and adds a market-risk charge.

Reduced BA-CVA: nothing counts

The reduced version of the basic approach is a formula on exposure at default, maturity and a sector risk weight, with no hedge term (MAR50.14 to 50.16). Every CVA hedge a bank on the reduced approach runs is outside the CVA calculation and inside the trading book. Hedging CVA under the reduced approach raises total capital.

That is why many banks on the reduced approach do not hedge CVA at all. They carry the volatility of CVA in profit and loss, and hold capital against the risk without any offset. Some say so in their own Pillar 3 disclosures.

Full BA-CVA: credit-spread hedges only

The full version adds a hedged component (MAR50.17 to 50.26).

Eligible instruments: single-name CDS, single-name contingent CDS and index CDS (MAR50.18). Rate, FX, equity and commodity hedges are never eligible under BA-CVA.
Eligible names: a single-name hedge counts if it references the counterparty, a legally related entity, or an entity in the same sector and region (MAR50.19).
How much it counts: the correlation between the hedge and the counterparty’s spread is 100% for a hedge on the counterparty itself, 80% for a legally related entity and 50% for an entity sharing sector and region (MAR50.26, Table 2); an index hedge’s risk weight is scaled by 0.7 where its constituents share sector and credit quality (MAR50.24).
A floor on the benefit: the final charge is a quarter of the reduced charge plus three quarters of the hedged one (MAR50.20), so even a perfect credit hedge leaves a quarter of the unhedged charge.

The hedged number nets single-name hedges against each counterparty’s stand-alone charge, takes index hedges off the systematic part, and adds a term for hedges that do not match the counterparty exactly (MAR50.21):

K_{\text{hedged}}=\sqrt{\Big(\rho\sum_c\big(\mathrm{SCVA}_c-\mathrm{SNH}_c\big)-\mathrm{IH}\Big)^2+\big(1-\rho^2\big)\sum_c\big(\mathrm{SCVA}_c-\mathrm{SNH}_c\big)^2+\sum_c \mathrm{HMA}_c}

K_{\text{full}}=\beta\,K_{\text{reduced}}+(1-\beta)\,K_{\text{hedged}},\qquad \beta=0.25

Here $\mathrm{SNH}_c$ is the recognised single-name hedging of counterparty $c$ , weighted by its correlation with the counterparty, $\mathrm{IH}$ the index hedges, and $\mathrm{HMA}_c$ the part of the single-name hedges that does not offset, which grows as that correlation falls.

The exposure side stays unhedged in capital terms. A bank whose CVA moves mostly with rates or FX gets little from the full approach.

SA-CVA: both sides count

The standardised approach capitalises the sensitivities of regulatory CVA to six risk classes, so a hedge counts where its sensitivity offsets CVA’s.

Eligible instruments: those that hedge the variability of the counterparty credit spread and those that hedge the exposure component (MAR50.38). Only whole transactions used to mitigate CVA risk, and managed as such, qualify (MAR50.37); instruments not eligible for the internal models approach for market risk, such as tranched credit derivatives, do not (MAR50.39).
How much it counts: a hedge enters the same bucketed calculation with the opposite sign, and offsets CVA’s sensitivity to the same risk factor. A hedging disallowance parameter, R = 0.01, stops the offset from being perfect (MAR50.53).
What it takes: CVA sensitivities to every supervisory risk factor for the whole book and its hedges, at least monthly, and a CVA desk or equivalent function that manages CVA risk and its hedges (MAR50.28 and 50.30), with supervisory approval.

Under SA-CVA the same rate swap that adds market-risk capital under the basic approach comes out of the market-risk calculation and reduces the CVA charge.

Side by side

	Reduced BA-CVA	Full BA-CVA	SA-CVA
Counterparty CDS	Not recognised; market-risk capital	Recognised, 100% correlation	Recognised
CDS on a related name or same sector and region	Not recognised	Recognised, 80% or 50%	Recognised, through the sensitivity
Index CDS	Not recognised	Recognised, index scalar 0.7 where applicable	Recognised
Rate, FX, equity, commodity hedges of the exposure	Not recognised	Not recognised	Recognised
Effect of hedging on total capital	Raises it	Lowers the CVA charge, floored at a quarter; exposure hedges raise it	Lowers it, R = 0.01
What the bank must compute	Exposure at default per netting set	The same, plus hedge mapping	CVA sensitivities for book and hedges, at least monthly

What this means for a bank deciding

The approach decides the hedging policy, not the other way round. A bank on the reduced approach that starts hedging CVA pays more capital; the same programme under SA-CVA saves it.
The question to answer is joint: what SA-CVA gives on the book as it stands, and what SA-CVA plus a hedging programme would give, against the basic approach today.
The calculation is the obstacle. Recognising exposure hedges needs CVA sensitivities to every supervisory risk factor for the book and the hedges together, which on many systems is a long batch run.

Norma’s Capital Study computes both approaches on an agreed scope of your book, with and without hedge recognition, within days of clean data.

Request the Capital Study Read nextSA-CVA or BA-CVA: how to decide on your own book

Sources

Basel Committee, MAR50, Credit valuation adjustment framework, paragraphs 50.10 to 50.26, 50.28 to 50.30, 50.37 to 50.39 and 50.53
Basel Committee, Targeted revisions to the credit valuation adjustment risk framework, July 2020

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