FRM Exam Part II · Credit Value Adjustment

CVA Hedging, Capital Charges and FVA, KVA, MVA

Updated 11 October 2026 · Fact-checked

CVA hedging, capital and funding adjustments describe how a bank manages the price of counterparty credit risk. The CVA desk buys CDS protection sized to expected exposure, holds Basel III CVA capital against spread losses, and charges FVA, MVA and KVA for funding, margin and capital costs. Match each question to the risk, hedge, charge or cost.

Understand CVA Hedging, Capital and Funding Adjustments

CVA is the market price of counterparty default risk on derivatives. It is the expected loss from a counterparty defaulting, adjusted to today's value. It moves every day because exposure and the counterparty's credit spread move every day. That makes it a trading risk, not just a credit risk.

Most large banks run a CVA desk. Trading desks pass their counterparty risk to it. The desk charges each trade a CVA fee through internal transfer pricing. In return it manages the resulting P&L swings by hedging. It also manages the capital the CVA risk consumes.

The main hedge for the credit spread part of CVA is a CDS on the counterparty. The bank buys protection. If the counterparty's spread widens, CVA rises (a loss), and the CDS gains. The hedge is never perfect. CDS notional is fixed, but exposure is random and changes as markets move. So the bank also hedges the market risk drivers of exposure, such as interest rates or FX. Many counterparties have no liquid single-name CDS. The desk then uses an index CDS or a proxy name, which leaves basis risk. Wrong-way risk makes it worse: exposure and default probability rise together.

Under Basel III, the CVA capital charge was added because, in the crisis, most counterparty credit losses came from CVA mark-to-market losses, not from actual defaults. The revised framework offers the standardised approach (SA-CVA), which needs supervisory approval and is sensitivity based, and the basic approach (BA-CVA), in a reduced version with no hedge recognition and a full version that recognises eligible hedges. Only eligible hedges, mainly single-name and index CDS, reduce the charge.

CVA is only part of the story. FVA is the cost or benefit of funding uncollateralised derivative positions at the bank's own funding spread. MVA is the cost of funding initial margin over the life of a trade. KVA is the cost of holding regulatory capital over the life of a trade, measured at the shareholders' required return. Together with CVA they form the XVA family. Whether FVA belongs in accounting fair value is debated, because it depends on the bank's own funding, not on market prices alone.

Key formulas to remember

Unilateral CVA (discrete sum): CVA = LGD × Σ [ DF(tᵢ) × EE(tᵢ) × PD(tᵢ₋₁, tᵢ) ]; LGD = 1 − recovery. EE is expected exposure (positive part only). PD is the marginal default probability in each interval, under risk-neutral measure.
Credit triangle: λ ≈ s ÷ LGD; s is the CDS spread, λ the hazard rate. Use for a quick risk-neutral PD when the question gives a spread.
Marginal PD from a hazard rate: PD(tᵢ₋₁, tᵢ) = e^(−λ·tᵢ₋₁) − e^(−λ·tᵢ); Gives default probability within one period, for use in the CVA sum.
Approximate CVA with flat inputs: CVA ≈ s × EPE × risky annuity; Flat spread and flat exposure. It is the basis for sizing a CDS hedge quickly.
CDS hedge notional (spread hedge): Notional ≈ CS01 of CVA ÷ CS01 per unit of CDS notional; With a maturity-matched CDS and flat inputs this is roughly the EPE. It is only a hedge of spread risk, not of exposure changes.
BA-CVA reduced version: Capital = DS × K_reduced, with DS = 0.65; DS is the discount scalar. The reduced version gives no credit for hedges.
FVA (approximate): FVA ≈ funding spread × EPE × T − funding spread × ENE × T; The first term is the funding cost on positive exposure. The second is the benefit on negative exposure (ENE). Discounting ignored.
MVA (approximate): MVA ≈ funding spread × average expected initial margin × T; Applies to margin posted that the bank must fund.
KVA (approximate): KVA ≈ hurdle rate × average expected capital × T; Capital is regulatory capital over the trade life. The hurdle rate is the shareholders' required return, often net of what capital earns.

How to solve CVA Hedging, Capital and Funding Adjustments questions

Use the same sequence for any CVA hedging, capital or XVA question. It stops you mixing up which adjustment or hedge the question is really about.

1Identify what is being asked: a CVA amount, a hedge size, a capital rule, or an XVA type (FVA, MVA, KVA).
2For a CVA amount, list EE, marginal PD and discount factor per period. Use LGD = 1 − recovery. Multiply, sum, then multiply by LGD.
3For a hedge, separate the two drivers. Credit spread risk is hedged with CDS. Exposure risk is hedged with rate, FX or other market instruments.
4Size a CDS hedge from the CS01: CVA CS01 divided by the CS01 per unit of CDS notional. With flat inputs this is about EPE.
5State the hedge limits: stochastic exposure, proxy or index basis, wrong-way risk, and CDS liquidity.
6For capital, name the approach (SA-CVA, BA-CVA reduced or full), say whether hedges count, and say they must be eligible.
7For XVA, match the cost to its source: funding of uncollateralised exposure is FVA, funding initial margin is MVA, capital held is KVA.
8Check direction and sign: widening spread raises CVA, a bought CDS gains, and a higher funding spread raises FVA.

Quickest way: Match the cost to its source

When to use it: Use this on conceptual MCQs where you must pick the right adjustment, hedge or capital treatment fast.

Ask: what is the money being paid for? Default risk is CVA. Funding of uncollateralised exposure is FVA. Funding of posted initial margin is MVA. Holding capital is KVA.
Ask: what moves the P&L? Counterparty spread moves are hedged with CDS. Moves in exposure drivers need market hedges.
Ask: does the hedge count for capital? Only eligible hedges do, and the reduced BA-CVA gives no recognition.
For numbers, do LGD × Σ(EE × PD) and stop. Do not add extra steps the question did not ask for.
Eliminate options that call a CDS hedge perfect or that reverse a sign.

Common mistakes in CVA Hedging, Capital and Funding Adjustments

Using recovery rate instead of LGD in the CVA formula.
Both numbers appear in the question and recovery is stated first.
Fix: Always convert: LGD = 1 − R. Write it down before you multiply.
Treating a CDS as a full hedge of CVA.
Students focus on spread risk and forget exposure is stochastic.
Fix: Say a CDS hedges spread risk only. Exposure changes, gap risk and wrong-way risk stay open, so market hedges are also needed.
Assuming any hedge reduces the CVA capital charge.
Students link economic hedging with regulatory relief.
Fix: Only eligible hedges count, mainly single-name and index CDS, and the reduced BA-CVA gives no hedge credit.
Mixing up FVA, MVA and KVA.
All three are funding or cost adjustments and have similar-sounding names.
Fix: Tie each to one source: uncollateralised exposure funding (FVA), initial margin funding (MVA), capital held (KVA).
Including negative exposure in the CVA sum.
Students use the mark-to-market itself instead of the positive part.
Fix: Use expected positive exposure. A negative value is the bank's liability and belongs in DVA or the funding benefit, not CVA.
Thinking CVA capital covers default losses.
CVA sounds like a credit loss measure.
Fix: The CVA charge covers mark-to-market losses from spread changes. Default risk on the same exposure is covered by the separate counterparty credit risk charge.

Worked examples

Example 1

A bank has a 3-year swap with a corporate. Expected positive exposures at years 1, 2 and 3 are $10 million, $12 million and $8 million. Marginal default probabilities for the three years are 2.0%, 2.5% and 3.0%. Recovery is 40%. Ignoring discounting, what is the unilateral CVA? (A) $296,000 (B) $444,000 (C) $540,000 (D) $740,000

Show the solution

LGD = 1 − 0.40 = 0.60.
Year 1: 10 × 0.020 = 0.200 million.
Year 2: 12 × 0.025 = 0.300 million.
Year 3: 8 × 0.030 = 0.240 million.
Sum = 0.740 million.
CVA = 0.60 × 0.740 = 0.444 million = $444,000.
Check the traps: $740,000 forgets LGD. $296,000 uses recovery (0.40) instead of LGD. $540,000 uses the peak exposure with the total PD.

Answer: (B) $444,000

Example 2

A CVA desk faces a counterparty with a flat EPE of $15 million over 5 years. The CDS spread is 200 bp and the risky annuity is 4.2. Using the approximation CVA ≈ s × EPE × risky annuity, what notional of 5-year CDS protection hedges the spread sensitivity of CVA? (A) $9 million (B) $15 million (C) $25 million (D) $63 million

Show the solution

CVA ≈ 0.02 × 15 × 4.2 = $1.26 million.
CVA CS01: a 1 bp rise in spread adds 0.0001 × 15 × 4.2 = $0.0063 million = $6,300.
CDS CS01 per $1 million notional: 0.0001 × 4.2 × 1,000,000 = $420.
Notional = 6,300 ÷ 420 = 15, so $15 million.
So with flat inputs the CDS notional equals the EPE. Do not multiply by LGD.
Limits: the hedge fixes spread risk only. If exposure rises, the hedge is too small. If exposure falls, the bank is over-hedged. Index or proxy hedges would add basis risk.

Answer: (B) $15 million

Exam tips

Expect conceptual MCQs: which hedge, which adjustment, which capital approach. Know the one-line definition of each of FVA, MVA and KVA.
When a question asks why a CDS hedge is imperfect, list stochastic exposure, basis risk from proxies, wrong-way risk and illiquidity.
Name the Basel framework precisely: SA-CVA or BA-CVA, reduced or full. Say which recognises hedges.
In calculation questions, check whether discounting is requested. If not stated, follow the data given and do not add it.
Remember the capital logic: the CVA charge exists because most crisis-era counterparty losses were mark-to-market, not defaults.

Practice questions from Credit Value Adjustment

CVA Hedging, Capital and Funding Adjustments: frequently asked questions

How do you hedge CVA with credit default swaps?

The CVA desk buys CDS protection on the counterparty, sized to the CVA's credit spread sensitivity, which is roughly the expected exposure for a matched maturity. If spreads widen, CVA rises and the CDS gains. The desk also hedges exposure drivers such as rates or FX, because CDS notional is fixed while exposure moves.

What is the Basel III CVA capital charge?

It is a capital requirement for the risk of mark-to-market losses on derivatives from changes in counterparty credit spreads. The revised framework uses SA-CVA, which needs supervisory approval, or BA-CVA, in reduced and full versions. Only eligible hedges can lower the charge, and the reduced BA-CVA gives no hedge recognition.

What is the difference between FVA, MVA and KVA?

FVA is the cost or benefit of funding uncollateralised derivative positions at the bank's funding spread. MVA is the cost of funding initial margin posted over a trade's life. KVA is the cost of holding regulatory capital against the trade, measured at the shareholders' required return.

What does the CVA desk do in a bank?

It takes counterparty credit risk from trading desks, charges them a CVA fee, and manages the resulting volatility by hedging. It uses CDS for spread risk and market instruments for exposure risk. It also monitors the capital the CVA positions use and the limits of its hedges.