FRM Exam Part II · Derivatives

Credit Valuation Adjustment (CVA) and DVA Explained

Updated 11 October 2026 · Fact-checked

CVA is the market value of counterparty default risk on a derivative. Unilateral CVA ≈ LGD × Σ EE(tᵢ) × discount factor × marginal default probability over each period. DVA is the same calculation using your own default risk and the counterparty's exposure to you. Bilateral CVA = CVA − DVA.

Understand Credit Valuation Adjustment (CVA) and DVA

A derivative priced as if both sides will always pay is a risk-free value. In reality, if your counterparty defaults while the contract is worth a positive amount to you, you lose part of that value. Credit valuation adjustment (CVA) is the price of that risk. It is deducted from the risk-free value.

CVA depends on three things. First, exposure: how much you would be owed if default happened at a given date. Only positive values count, because if the contract is a liability to you, you still owe it. Second, default probability: the chance the counterparty defaults in each period, usually taken from CDS spreads or bond spreads, so it is risk-neutral. Third, loss given default (LGD = 1 − recovery rate): the fraction you do not get back.

Because exposure changes over time, you build an expected exposure (EE) profile and sum across dates. Each date's loss is discounted and weighted by the probability that default occurs in that interval. A common simplification assumes exposure and default are independent. That assumption fails under wrong-way risk, where exposure rises as the counterparty's credit worsens. Then CVA is higher than the independent formula gives.

Debit valuation adjustment (DVA) looks at the other side. Your counterparty also faces the risk that you default when the contract is worth a positive amount to them. This is a benefit to you, because it reduces what you owe in value terms. DVA uses your own default probability and the expected negative exposure (ENE). Bilateral CVA is CVA minus DVA. DVA is controversial: your value rises when your own credit worsens, which you cannot realise unless you default. Because of this, regulators do not give capital credit for DVA.

Key formulas to remember

Unilateral CVA (discrete): CVA = LGD × Σ [ EE(tᵢ) × DF(tᵢ) × PD(tᵢ₋₁, tᵢ) ]; Assumes exposure is independent of default. PD is the marginal default probability in each interval. LGD = 1 − R.
Marginal default probability: PD(tᵢ₋₁, tᵢ) = Q(tᵢ₋₁) − Q(tᵢ); Q(t) is survival probability to t. With constant hazard rate λ, Q(t) = e^(−λt).
Credit triangle approximation: λ ≈ s ÷ LGD; s is the CDS spread as a decimal. A rough way to get the hazard rate from a spread.
DVA: DVA = LGD(own) × Σ [ ENE(tᵢ) × DF(tᵢ) × PD(own)(tᵢ₋₁, tᵢ) ]; ENE uses the absolute size of negative exposure. It is a positive number that adds to value.
Bilateral CVA and value: Bilateral CVA = CVA − DVA; Value = Risk-free value − CVA + DVA; The bilateral adjustment is the net of both.
Rough unilateral CVA for a flat exposure: CVA ≈ EPE × LGD × (1 − Q(T)); Ignores discounting. Good for quick estimates.

How to solve Credit Valuation Adjustment (CVA) and DVA questions

Use this order for any CVA or DVA question. It keeps exposure, default and recovery separate so you do not mix them.

1Identify whose default is being priced. For CVA it is the counterparty and you use positive exposure (EE). For DVA it is your own default and you use negative exposure (ENE).
2List the time buckets and the expected exposure at each date. Check that exposure is positive-only for CVA.
3Find the survival probability or hazard rate. If given a spread, use λ ≈ s ÷ LGD, then Q(t) = e^(−λt).
4Compute marginal default probability per bucket as Q(tᵢ₋₁) − Q(tᵢ).
5Compute LGD = 1 − recovery rate and the discount factor for each date.
6Multiply EE × DF × marginal PD for each bucket, sum, then multiply by LGD.
7For bilateral CVA, repeat with own-default data and ENE, then subtract DVA from CVA.
8Check the sign and the story: CVA reduces value, DVA raises it, and wrong-way risk pushes CVA up.

Quickest way: Short-cut for constant exposure and hazard rate

When to use it: Use when the question gives a flat or single exposure and either default probabilities or a spread, and options differ by sizeable amounts.

Take the single EE (or average EPE) as the exposure.
Get cumulative default probability: 1 − Q(T), either given or from 1 − e^(−λT).
Multiply: EPE × LGD × cumulative PD.
Adjust slightly down if discounting is mentioned.
If the question asks for the net bilateral figure, do the same for DVA and subtract.

Common mistakes in Credit Valuation Adjustment (CVA) and DVA

Using total exposure including negative values in CVA.
Students use the mark-to-market value directly without flooring at zero.
Fix: CVA uses positive exposure only. Negative values feed DVA through ENE.
Forgetting to multiply by LGD, or using recovery rate in its place.
Both numbers are given in the question, and recovery is the one stated.
Fix: Always compute LGD = 1 − R first and write it down.
Using cumulative default probability for each bucket instead of marginal.
Survival or cumulative figures are given in tables and look ready to use.
Fix: Subtract successive survival probabilities to get the probability of default within each interval.
Adding DVA to CVA, or applying the wrong sign.
Both are called adjustments, so students lose track of direction.
Fix: Value = risk-free value − CVA + DVA. Bilateral CVA = CVA − DVA.
Treating wrong-way risk as lowering CVA.
Confusion with right-way risk or with diversification.
Fix: Wrong-way risk means exposure is high when default is likely, so CVA is higher than the independence formula. Right-way risk lowers it.
Saying DVA is a genuine hedgeable gain that regulators recognise in capital.
It appears as a legitimate accounting figure.
Fix: Remember DVA gains arise when your own credit worsens and cannot be monetised without default. Regulatory capital does not give credit for it.

Worked examples

Example 1

A 2-year swap has expected exposure to the counterparty of USD 4 million at year 1 and USD 3 million at year 2. Discount factors are 0.96 and 0.92. The counterparty's survival probabilities are 0.98 at year 1 and 0.94 at year 2 (Q(0)=1). Recovery is 40%. Compute unilateral CVA, assuming independence.

Show the solution

LGD = 1 − 0.40 = 0.60.
Marginal PD year 1 = 1 − 0.98 = 0.02. Marginal PD year 2 = 0.98 − 0.94 = 0.04.
Year 1 term: 4,000,000 × 0.96 × 0.02 = 76,800.
Year 2 term: 3,000,000 × 0.92 × 0.04 = 110,400.
Sum = 187,200.
CVA = 0.60 × 187,200 = 112,320.

Answer: CVA ≈ USD 112,320.

Example 2

A bank has an average expected positive exposure of EUR 10 million to a counterparty over one year, and the counterparty's one-year cumulative default probability is 3%, with recovery 25%. The bank's own expected negative exposure is EUR 6 million, and its own one-year cumulative default probability is 1%, with recovery 40%. Ignore discounting. Compute bilateral CVA.

Show the solution

CVA: LGD = 0.75. CVA = 10,000,000 × 0.75 × 0.03 = 225,000.
DVA: LGD = 0.60. DVA = 6,000,000 × 0.60 × 0.01 = 36,000.
Bilateral CVA = 225,000 − 36,000 = 189,000.
Value of the position is reduced by EUR 189,000 relative to the risk-free value.

Answer: Bilateral CVA = EUR 189,000 (CVA 225,000 minus DVA 36,000).

Exam tips

Read which side the question asks about. CVA uses EE and counterparty PD. DVA uses ENE and your own PD.
Compute marginal default probabilities from survival figures before anything else. This is the most common calculation trap.
For conceptual questions, link wrong-way risk to higher CVA and explain why independence understates it.
Know why DVA is criticised: it creates gains as your own credit deteriorates and regulators do not allow it in capital.
If options are close, check whether discounting is meant to be included. If the question says to ignore it, do not apply discount factors.

Practice questions from Derivatives

Credit Valuation Adjustment (CVA) and DVA in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

CFA Level IIValuing Risky Bonds and Credit Valuation Adjustment

Credit Valuation Adjustment (CVA) and DVA: frequently asked questions

What is the CVA formula for FRM Part II?

CVA = LGD × Σ EE(tᵢ) × DF(tᵢ) × marginal PD(tᵢ₋₁, tᵢ). It assumes exposure is independent of default. Compute each bucket, sum, then multiply by LGD.

What is the difference between CVA and DVA?

CVA prices the risk that the counterparty defaults while owing you, and it reduces the derivative value. DVA prices the risk that you default while owing the counterparty, and it raises your reported value. Bilateral CVA is CVA minus DVA.

How does wrong-way risk affect CVA?

Wrong-way risk occurs when exposure to a counterparty rises as its credit quality falls. This makes losses given default larger than an independent calculation suggests, so CVA is higher. Right-way risk has the opposite effect.

Where do default probabilities for CVA come from?

They are usually implied from CDS spreads or bond spreads, so they are risk-neutral. A rough link is hazard rate ≈ spread ÷ LGD. Historical default rates are not used for pricing CVA.