The XVA Family: FVA, MVA, KVA

You already know CVA — the price of the chance your counterparty defaults — and its mirror image DVA, the (controversial) credit you take for the chance you default. Good. Now meet the rest of the family. Because after 2008, the quants on the trading floor figured out something uncomfortable: default risk was only the first wedge between the clean textbook price and the price a desk actually has to charge. There were more. Funding the position costs money. Posting margin costs money. The regulatory capital a trade ties up costs money. Each of those got its own adjustment, its own three-letter acronym ending in “VA,” and its own desk to manage it. This lesson is the whole alphabet soup — FVA, MVA, KVA, ColVA — and, crucially, how they stack into the single number that turns 100 into the price you quote.

From CVA to XVA: the alphabet soup

Analogy. The textbook price of a derivative is the sticker price on a car — clean, headline, the number in the ad. But nobody drives off the lot paying the sticker. There’s tax, there’s the registration fee, there’s the financing cost if you borrowed, there’s insurance you’re forced to carry. None of those are “the car”; they’re the cost of actually owning and operating the car in the real world. XVA is the dealer’s out-the-door price for a derivative — sticker plus every unavoidable real-world cost of carrying the position on a real balance sheet.

The definition. XVA isn’t one thing — it’s a family name. The “X” is a wildcard standing in for any letter, and the “VA” means valuation adjustment: a signed correction applied to the risk-free, textbook value of a derivative to get the price a bank can actually live with. The members you’ll meet:

The mental model that organises the whole zoo: CVA and DVA price default. Everything else prices funding, margin, and capital. That’s the cleanest way to keep them straight — if an adjustment is about “will someone fail to pay,” it’s CVA/DVA; if it’s about “what does it cost me to hold and carry this thing,” it’s one of the new ones.

Pitfall. People hear “XVA” and assume it’s a single, agreed-upon number you bolt on. It isn’t. The family is additive but contested — desks disagree about whether DVA is even real, whether FVA double-counts it, and how to charge KVA to a client. XVA is less a formula and more a negotiation between accounting, funding, and the regulator, dressed up in acronyms.

FVA: the cost of funding the position

Analogy. Imagine a friend owes you $10,000, payable in two years, and is rock-solid good for it. Wonderful — except you needed that $10,000 now, so you borrowed it from the bank at interest. You’ll get paid back eventually, but in the meantime you’re paying interest to carry a loan against money you don’t yet have. The interest you bleed while waiting is exactly FVA: the cost of funding a position whose value hasn’t turned into cash yet.

The definition. When a trade is uncollateralised (or imperfectly collateralised), its mark-to-market isn’t matched by cash posted back and forth. So the bank must fund that mark out of its own borrowing, at a funding spread over the risk-free rate. The funding valuation adjustment (FVA) is the present value of that lifetime funding cost. It splits into two halves:

FVA = FCA − FBA.

• FCA (funding cost adjustment) applies when you’re a net asset — the trade is in your favour, you must fund the receivable, and that costs you. A charge.
• FBA (funding benefit adjustment) applies when you’re a net liability — you owe, which means you’re effectively being funded by the position, a benefit.

Worked example. Take a single uncollateralised trade with an expected exposure of $10m, an average life of about 2 years, funded at a funding spread of 50 basis points (0.50%) over the risk-free rate. The funding cost, to a first approximation, is just spread × exposure × time:

$\text{FVA} \approx \$10\text{m} \times 0.0050 \times 2 = \$100{,}000.$

So carrying that one winning trade quietly costs the desk about $100k in funding over its life — money that never appears in the textbook price, but absolutely appears in the desk’s P&L. (The real calculation integrates the expected positive exposure profile over time rather than using a flat $10m, but the intuition — spread × exposure × life — is exactly this.)

Pitfall — the FVA/DVA double-count. Here’s the controversy that ate a thousand quant-desk arguments. FBA (the funding benefit when you owe) and DVA (the credit you take for your own default risk) overlap: both reward you, in part, for your own credit being risky. Count both in full and you’re booking the same benefit twice. The reconciliation is subtle and firms still disagree, but the rule of thumb is: if you already recognise DVA, you can’t also pocket the full FBA without double-counting your own riskiness.

When it matters

FVA bites hardest on long-dated, deeply one-directional, uncollateralised trades — think a 10-year swap with a corporate client who posts no collateral. Perfectly collateralised trades (daily cash variation margin both ways) have near-zero FVA, because the collateral is the funding. Hold that thought: collateralisation is the lever that turns most of this family on and off.

MVA: funding the initial margin

Analogy. MVA is the security deposit on a long lease. When you rent, you hand the landlord a deposit that just sits there for the whole tenancy — you can’t spend it, it’s not really earning for you, and you only get it back at the end. If you had to borrow that deposit, you’d pay interest on it the entire lease. Initial margin is that deposit; MVA is the interest you pay to fund it for the life of the trade.

The definition. Recall from the netting-and-collateral lesson that initial margin (IM) is a defensive buffer — posted up front, sized to cover potential future exposure over a close-out period — and it’s now mandatory for cleared trades and for uncleared trades caught by the bilateral margin rules (the “UMR”). Unlike variation margin, which flows back and forth and roughly nets to zero, IM is locked away for the trade’s whole life. The margin valuation adjustment (MVA) is the present value of the lifetime funding cost of that posted initial margin.

Worked example. Suppose a portfolio of trades requires you to post, on average, $5m of initial margin over a 5-year life, funded at the same 50bp spread:

$\text{MVA} \approx \$5\text{m} \times 0.0050 \times 5 = \$125{,}000.$

Notice the shape: small per year ($25k/year here) but it compounds with maturity — double the tenor and you roughly double the MVA, because the deposit stays locked up twice as long. On a single short trade MVA is a rounding error; on a 20-year book of swaps it’s a serious number.

The driver — SIMM/IM size. What sets the IM amount? For uncleared trades, it’s typically the industry-standard SIMM (Standard Initial Margin Model); for cleared trades, the CCP’s own IM model. Both size IM off the portfolio’s risk — more risk, bigger IM, bigger MVA. So MVA isn’t a fixed fee; it’s driven by how much margin the model demands, which is why netting and risk-reducing trades quietly shrink your MVA bill.

Pitfall. Don’t conflate MVA with FVA. FVA funds the variation side — the trade’s mark-to-market. MVA funds the initial margin — a separate, static buffer on top. A trade can have tiny FVA (well-collateralised mark) yet meaningful MVA (because the CCP still demands a fat IM buffer). They’re different pots of cash being funded for different reasons.

KVA: the cost of regulatory capital

Analogy. KVA is the opportunity cost of the chips you’re forced to keep on the table. A casino makes the house keep a reserve so it can always pay out winners. That reserve isn’t lost — but it’s stuck, and the casino’s owners could have invested it elsewhere for a fat return. They demand that the table earns enough to justify locking up those chips. Regulatory capital is the reserve; the shareholders’ required return is the hurdle rate; KVA is the cost of clearing that hurdle over the trade’s life.

The definition. Every derivative consumes regulatory capital — the bank must hold loss-absorbing equity against it, principally the counterparty-credit-risk (CCR) capital charge and the separate CVA capital charge (yes, CVA generates its own capital requirement on top of the CVA you book). That capital is expensive equity, and shareholders demand a return on it — the hurdle rate, typically well above the funding rate. The capital valuation adjustment (KVA) is the present value of the lifetime cost of holding that regulatory capital — i.e., what it costs to pay shareholders their required return on the equity the trade ties up.

Worked example. Suppose a long-dated uncollateralised trade ties up, on average, $2m of regulatory capital over its life, the shareholders’ hurdle rate is 10%, and the bank funds at, say, 3% — so the excess return capital must earn above funding is about 7%. Over an average capital-weighted life of 5 years:

$\text{KVA} \approx \$2\text{m} \times 0.07 \times 5 = \$700{,}000.$

Stack that against the earlier numbers — FVA ≈ $100k, MVA ≈ $125k — and you see why KVA is frequently the single biggest member of the family on long-dated, uncollateralised, capital-hungry trades. The capital is large, the hurdle is steep, and the life is long; the three multiply.

Pitfall — the most contested charge to bill a client. KVA is the most model-dependent and politically fraught of the family. Capital requirements depend on the regulatory regime, internal-vs-standardised models, and future rules that haven’t even been written yet (capital projected over a 30-year swap depends on guessing 2040’s regulation). And charging a client an explicit KVA on day one — essentially “you owe us our shareholders’ return” — is a hard sell competitively. Many desks compute KVA for internal pricing and hurdle decisions but shade how much of it they actually pass to the client.

ColVA and the loose ends

Analogy. You’ve paid off most of the bill — but there’s always that fiddly line at the bottom of the receipt: a currency-conversion fee, an oddment of rounding, a “you could’ve used the other coupon” footnote. ColVA is the family’s fiddly bottom line — small, technical, but real, and the place where the cleverest desks squeeze out an extra basis point.

The definition. The collateral valuation adjustment (ColVA) corrects for collateral that earns a rate different from the discount rate, or for non-cash / wrong-currency collateral. It shows up two ways:

• Rate mismatch. Your CSA (the collateral agreement) may pay interest on posted cash at one rate, while standard practice discounts the trade’s flows at another (e.g. an OIS curve). The gap, summed over the life, is a ColVA.
• CSA optionality / cheapest-to-deliver. Many CSAs let the posting party choose which currency or asset to post. Rational posters deliver whatever is cheapest to fund at the time — an embedded option that has value, and that value is a ColVA.

Pitfall. ColVA is usually small, so people ignore it — but on huge, long-dated, multi-currency collateralised books it adds up, and mishandling CSA discounting (using the wrong curve) quietly mis-marks the whole portfolio. The “small” adjustment is small per trade, not per franchise.

When it matters — and the family keeps growing

ColVA matters most where there’s collateral optionality and currency choice — big interbank books under multi-currency CSAs. And it’s a fitting note to end the roll-call on, because the family is still expanding: discounting choices (the OIS-vs-other debate), liquidity adjustments (LVA), and others keep getting proposed. The “X” in XVA is a wildcard for a reason — whenever someone finds a new real-world cost the textbook price ignores, they coin a new “VA” and bolt it onto the stack.

The XVA waterfall: risk-free → all-in

Now assemble the whole stack. Start from the risk-free value — the clean textbook number, set here at 100 — and walk down (mostly) through each adjustment until you reach the price the desk actually quotes. This is the payoff of the entire lesson: watch the wedges accumulate.

The canonical bilateral numbers, in price points per 100 of value:

$100 \;\underbrace{-\,0.80}_{\text{CVA}} \;\underbrace{+\,0.50}_{\text{DVA}} \;\underbrace{-\,0.40}_{\text{FVA}} \;\underbrace{-\,0.30}_{\text{MVA}} \;\underbrace{-\,0.50}_{\text{KVA}} \;=\; 98.50.$

That’s a net XVA of −1.50 points and an all-in price of 98.50 — the textbook said 100, the desk charges 98.50, and that 1.50-point gap is the XVA family, summed. Play with the island below: the bars float as a waterfall, each one a signed step, the dark bar at the end is the net.

Read the bilateral case. The two biggest wedges are CVA (−0.80) and KVA (−0.50) — default and capital — while DVA (+0.50) is the only thing handing value back. Funding and margin (FVA −0.40, MVA −0.30) fill in the middle. Net them and you’ve lost 1.50 points off the textbook price before you’ve earned a cent of spread.

Now flip to “Centrally cleared” and watch the shape transform. Push the same trade through a central counterparty (CCP) and:

• CVA collapses — a CCP is default-remote (mutualised default fund, member contributions), so the counterparty-default charge nearly vanishes.
• DVA collapses — symmetric; against a default-remote CCP, your own-default credit is moot.
• FVA collapses — the CCP takes daily variation margin, so the mark is collateralised and there’s little uncollateralised mark left to fund.

What’s left is mostly MVA — because the CCP still demands a fat initial margin you must fund for the trade’s life — plus a smaller KVA. The total shrinks, but it doesn’t hit zero. Clearing doesn’t delete XVA; it swaps default and funding risk for a margin-funding cost. Hold that — it’s the entire setup for the next lesson.

Why XVA reorganised the trading floor

XVA didn’t just add line items to a pricing sheet — it rewired how banks are organised. Because every adjustment is portfolio-level (a new trade’s CVA depends on its entire netting set, its FVA on the firm’s funding, its KVA on the firm’s capital), you can’t leave these to the individual product trader. So banks built centralised XVA desks: a single team that owns CVA, DVA, FVA, MVA, KVA and ColVA across the franchise, charges them to the product desks as an internal transfer price, and hedges the resulting sensitivities (buying CDS against CVA, managing funding and capital).

The upshot for you as a pricer: a derivative’s price is no longer just its discounted payoff. It’s the payoff, minus default, minus funding, minus margin, minus capital — a sum over the whole family. Master that and you’re pricing the way a real post-2008 desk prices.

Next — Wrong-Way Risk & Central Clearing — we just saw clearing reshape the XVA stack rather than erase it. But clearing introduces its own monster: wrong-way risk, where your exposure balloons at exactly the moment your counterparty is most likely to default. We’ll see why a CCP is “default-remote” but never “default-proof,” and what it costs you to find out.