xVA explained: CVA, DVA and FVA for banks

The 2008 crisis handed banks an uncomfortable discovery about their derivative books. The heaviest losses came not from counterparties actually defaulting but from the market repricing the risk that they might: day after day, the value of that risk moved against the banks holding it. The textbook derivative price, built on default-free counterparties and free funding, had left the biggest costs out, and the crisis collected them all at once.

The xVA family of valuation adjustments is the fix. CVA (credit valuation adjustment) prices the counterparty’s risk of default, DVA (debit valuation adjustment) prices the bank’s own, and FVA (funding valuation adjustment) prices the cost of funding the position. None of them is an exotic edge case. They are routine line items at any institution with material derivative exposure. Model validation, documentation and risk governance on those portfolios start from understanding how they relate to each other, rather than treating each as a separate quant problem.

Why pre-2008 pricing ignored default and funding

A derivative’s fair value, in a world of default-free counterparties and frictionless funding, is the present value of its expected cash flows discounted at the risk-free rate. Before 2008, this was how most dealer books were marked in practice, and the crisis broke the assumption from both sides at once. Counterparties could default before settlement. Dealers themselves were not risk-free either: adjusting for the counterparty’s credit risk while treating your own default probability as zero stopped being tenable.

A third gap followed as funding markets seized. Banks borrowing at a credit spread above the risk-free rate incur a real cost to finance uncollateralised derivative positions. By the early 2010s, major dealers were reporting that cost in their financial statements, and the figures were large enough to demand formal treatment.

xVA is the umbrella term for the adjustments that close these gaps: the counterparty’s risk of default, the bank’s own, and the cost of funding the position. CVA, DVA and FVA are the three that most directly affect fair-value accounting, regulatory capital, and trading decisions. They aren’t independent of one another, and the Basel framework doesn’t treat them all the same way.

CVA: pricing the counterparty’s default risk

The credit valuation adjustment (CVA) converts the risk-free value of a derivative into a price that reflects the counterparty’s risk of defaulting before settlement. The calculation walks the trade’s future. At each point in the trade’s life, ask how much the counterparty would owe if it defaulted then, weight that exposure by the probability of default at that point and by LGD (loss given default, the fraction not recovered), and discount back to today. The calculation also runs per counterparty, not per trade. When a counterparty fails, its trades offset each other and only the net is at risk; that group of trades is the netting set.

Neither main input is simply observable. Exposure has to be simulated across thousands of paths, because a derivative’s value swings with the market: the same swap can be owed to you at one point in its life and owed by you at another.

Default probability comes from credit spreads, the market’s live price on a counterparty’s risk, but those are only observable for the few names with liquid credit default swap markets; for the majority of corporate counterparties the spread is built from ratings-based proxies, under the hierarchy of rating, industry and region set out in the EBA’s RTS 2013/17 and adopted as Commission Delegated Regulation (EU) No 526/2014.¹ Most of a CVA number, in other words, is model rather than market.

Where CVA modelling most often goes wrong is wrong-way risk: the amount a counterparty owes you growing at the same moment their ability to pay shrinks. The two normally move independently; when they move together, the losses compound and CVA rises with them. The industry splits it in two. Specific wrong-way risk is built into a badly structured deal, the classic example being a trade collateralised with the counterparty’s own shares: the moment they are in trouble, the collateral is too. General wrong-way risk comes from the wider economy moving both at once, a downturn weakening the counterparty just as the trades against them move in your favour.

Accounting makes all of this mandatory. IFRS 13 defines fair value as "the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date".² No market participant pays full price for a promise from a counterparty that might default, so CVA is part of fair value at every reporting date. IFRS 13 also allows the risk to be measured on a net basis where the portfolio is managed and documented on that basis, which is why CVA runs at netting-set level in practice.

DVA: what accounting demands and capital forbids

The debit valuation adjustment (DVA) is the mirror image of CVA: the gain to the bank from the possibility that it defaults on its own derivative liabilities. Where CVA marks down what a counterparty owes you, DVA marks down what you owe them, because a defaulting bank would settle for less than the full amount. The effect produces famously odd optics in stressed quarters: a bank books an accounting gain precisely because its own creditworthiness has deteriorated.

CVA and DVA don’t net cleanly, though. Whichever party defaults first ends the trade, and only the survivor gets to claim, so the pricing has to track the order of default. Simply subtracting one number from the other is an approximation, and it degrades the more closely the two parties’ fortunes are linked.

Accounting requires DVA for the same reason it requires CVA: fair value must reflect every risk in the contract, the bank’s own included.³ The capital framework refuses it. MAR50, the Basel framework’s dedicated CVA chapter, is explicit that "regulatory CVA excludes the effect of the bank’s own default", and the CRR directs banks to filter own-credit gains out of capital before they reach the capital base.⁴ Stefan Walter, then secretary-general of the Basel Committee, put the reasoning plainly: "the potential for perverse incentives resulting from profit being linked to decreasing creditworthiness means capital requirements cannot recognise [DVA]".⁵

The result is a permanent gap, by design, between fair-value profit and loss (P&L) and the regulatory capital base. Accounting asks what a market participant would pay for the position today; capital asks what loss the bank can absorb as a going concern. DVA enters the first and not the second. For model validators this gap isn’t a defect in either framework: it is the central documentation challenge.

A single derivative portfolio therefore carries two CVA models. The accounting model prices the book as the market would, the bank’s own credit included, because that is what fair value means. The regulatory model computes the narrower number the capital rules define, own credit stripped out. Same trades, two definitions, two legitimate answers, and they have to be validated as two models, not one.

FVA: real cost, contested status

The funding valuation adjustment (FVA) is the cost of funding an uncollateralised trade, and it exists because banks borrow at a premium to the risk-free rate. A small example carries the whole idea. A dealer buys $100 million of T-bills, which earn the risk-free rate, and pays for them by borrowing $100 million for a year at the risk-free rate plus 50 basis points. The asset earns the risk-free rate; the borrowing costs more; the difference, $500,000, comes out of shareholders’ pockets. That shortfall, weighted by the chance the dealer is still around to pay it, is the FVA. The same arithmetic applies to any uncollateralised trade the bank funds with its own borrowing.

By end-2013 the numbers were large enough to force disclosure. JP Morgan reported a $1.5 billion FVA for the year. Bank of America Merrill Lynch, Morgan Stanley, and Citigroup each reported figures in the hundreds of millions in subsequent periods. The practice of disclosure stabilised.

Two camps disagree on FVA’s status, and that disagreement matters to practitioners because it decides how FVA should be treated in model documentation and P&L attribution. One camp, led by Pallavicini, Perini and Brigo, derives FVA from inside the pricing equation itself. Funding cash flows are real payouts of the contract, so FVA belongs in the price alongside CVA and DVA, and the equation’s recursive form is what makes "the introduction of a purely additive funding valuation adjustment (FVA) difficult". On the question of whether FVA is simply DVA under another name, they are blunt: "it is in general wrong to identify them with the DVA".⁵

The other camp, led by Andersen, Duffie and Song, concludes the opposite. FVAs, they argue, "are not actually components of the market values of the positions being financed. Instead, they are debt-overhang transfers from shareholders to creditors", so booking both FVA and DVA double-counts the same cash flows, because both ride on the bank’s own credit spread.⁶ The debate has not closed in the decade since.

Our steer, given a debate that will not close soon: treat FVA as a real cost when deciding whether an uncollateralised trade is worth doing, document which convention the book uses and why, and test explicitly for overlap with DVA. The danger isn’t choosing the wrong camp; it is counting the same spread twice.

Why the adjustments don’t simply add

CVA, DVA and FVA can’t be computed separately and added up. Each adjustment depends on the trade’s value, and the trade’s value depends on each adjustment, so the calculation loops: dealers run it iteratively until the price settles. It is what pricing looks like once funding costs and both parties’ default risk live inside the same equation.

Collateral changes the picture without ending it. A perfectly collateralised trade, cash posted daily with no minimum transfer amount against every move in its value, wipes out most CVA and DVA, because barely any credit risk survives a one-day window. It wipes out FVA on that exposure too, since the posted collateral earns a rate that offsets the funding cost.

What appears instead is a new funding question. ColVA (collateral valuation adjustment) prices the gap between the rate collateral earns and the rate the bank funds at; MVA (margin valuation adjustment) prices the cost of funding initial margin, whether that margin goes to a central counterparty on a cleared trade or to a counterparty under the uncleared margin rules.

Perfect collateralisation wipes out most of the bilateral credit risk that drives CVA and DVA, and the funding cost that drives FVA on that exposure, but it does not eliminate the xVA problem: it relocates it.

Only CVA attracts a capital charge

Of the full xVA family, only CVA enters the Basel regulatory capital framework. The Basel Committee on Banking Supervision’s revised CVA framework took effect internationally on 1 January 2023. EU banks apply it from 1 January 2025 under CRR3, and UK banks from 1 January 2027 under the Basel 3.1 implementation. The revised Basel CVA framework defines the exposure it charges for in its own terms: CVA risk is "the risk of losses arising from changing CVA values in response to changes in counterparty credit spreads and market risk factors that drive prices of derivative transactions and SFTs".⁴ DVA, FVA, KVA (capital valuation adjustment, the lifetime cost of holding regulatory capital against a trade) and MVA don’t enter the capital charge.

Two approaches are available. BA-CVA (the basic approach) is the default, open to all banks without specific supervisory permission. SA-CVA (the standardised approach) is a finer-grained calculation built from risk sensitivities and aligned with the Fundamental Review of the Trading Book (FRTB) market risk rules our FRTB guide covers⁷, available only with supervisory approval. Smaller books get relief: a bank whose non-centrally-cleared derivative notional stays at or below €100 billion can set its CVA capital equal to its counterparty credit risk charge and skip the separate calculation, unless its supervisor judges the CVA risk material.

The CVA feeding this charge is the narrower of the two: DVA stripped out, and, where market data is thin, a supervisory risk weight substituted under MAR50 rather than an observed spread. This is why the first question in any CVA model review is which of the two the model computes, the accounting CVA or the regulatory one. The accounting version must include DVA; the regulatory version must not.

The system, not the line item

CVA, DVA, and FVA each address a different gap in the risk-free derivative price. CVA captures the counterparty’s credit risk. DVA captures the dealer’s own credit risk. FVA captures the cost of funding the position. All three interact through the trade’s value, and the frameworks split them: accounting requires CVA and DVA and leaves FVA contested, while capital charges CVA alone.

For model validators, the questions are fixed: which CVA is in scope, whether wrong-way risk is captured, and how the model handles the recursive interaction with DVA and FVA. For risk teams pricing new trades, the action is to put FVA into the decision: an uncollateralised trade that only clears its hurdle before funding costs doesn’t clear it. For senior risk and finance leadership, the ask is one report that reads the xVA lines together, as live exposures to counterparty health, the bank’s own credit, and funding markets at once.

The crisis version of this system opened the piece; the ordinary version runs every quarter. A desk marks its swap book, the CVA line moves by more than the rate shift explains, the capital charge diverges from the accounting P&L, and an FVA figure lands in the board pack with a question mark against it. Nothing is broken. That is the system doing what it does.

One book, two CVAs, three adjustments: read them as a system, or explain them after the fact.

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