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FRM Exam Part II · Counterparty Risk and Beyond

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) × PD(ti-1, ti), using discounted expected exposure. DVA is the matching gain from your own default risk. Bilateral CVA = CVA − DVA. To solve, get exposure, default probability and recovery, then multiply and sum.

Understand Credit Valuation Adjustment (CVA) and DVA

A derivative with a risky counterparty is worth less than the same derivative with a risk-free one. The gap is the credit valuation adjustment (CVA). Risky value = risk-free value − CVA.

CVA only matters when you are owed money. If the counterparty defaults when the trade has positive value to you, you lose part of it. If the value is negative to you, you still owe it in full. So CVA depends on positive exposure, not net exposure. This is why you use expected exposure (EE) or discounted EE built from the positive part of the mark-to-market.

The unilateral approach assumes only the counterparty can default. CVA is the loss given default times the sum, over time buckets, of discounted expected exposure times the probability of default in that bucket. Default probabilities usually come from CDS spreads, so CVA is a market-implied (risk-neutral) number.

DVA (debit valuation adjustment) is the mirror image. Your own default could happen when you owe money, and your counterparty then loses. That lowers your liability, so it adds to your value. Bilateral CVA = CVA − DVA. DVA is controversial: your profit rises when your own credit worsens. It is hard to hedge, and Basel III removes DVA from regulatory capital.

Wrong-way risk means exposure rises when the counterparty's default probability rises, which raises CVA above the independent estimate. Right-way risk is the reverse. Standard formulas assume independence, so they miss both. CVA is hedged with CDS on the counterparty, and with market hedges for the exposure. Basel's CVA capital charge covers the volatility of CVA.

Key formulas to remember

Unilateral CVA (discrete)
CVA = LGD × Σ [ EE*(ti) × PD(ti-1, ti) ]
EE* is discounted expected positive exposure. LGD = 1 − recovery rate. Assumes exposure and default are independent.
DVA (discrete)
DVA = LGD(own) × Σ [ ENE*(ti) × PD(own)(ti-1, ti) ]
ENE is expected negative exposure, taken as a positive amount owed by you.
Bilateral CVA
Bilateral CVA = CVA − DVA
Adjusted value = risk-free value − CVA + DVA.
Marginal default probability
PD(ti-1, ti) = Q(ti-1) − Q(ti)
Q(t) is the survival probability.
Credit triangle approximation
Hazard rate λ ≈ CDS spread ÷ LGD
Survival Q(t) = e^(−λt). A rough link between spread and default probability.
Risky value
Risky value = Risk-free value − CVA
A long-only receivable has CVA charged. A payable has no CVA from your side.

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

Use this order for any CVA or DVA question, numerical or conceptual.

  1. 1Identify who can default and whether the question is unilateral or bilateral.
  2. 2Find the exposure profile: take only positive values for CVA and only negative values (as amounts owed) for DVA. Use discounted EE if given.
  3. 3Get default probabilities per period from survival probabilities, hazard rates or CDS spreads.
  4. 4Compute LGD = 1 − recovery rate.
  5. 5Multiply EE × PD for each period, sum the results, then multiply by LGD.
  6. 6For bilateral, compute DVA the same way with your own PD and ENE, then CVA − DVA.
  7. 7Adjust the value: risky value = risk-free value − CVA (+ DVA if bilateral).
  8. 8Check wrong-way or right-way risk wording and say which direction it moves CVA.

Quickest way: Sum-product shortcut

When to use it: When the question gives EE and marginal PD for a few periods and asks for a CVA number.

  1. Multiply each EE by its period PD, in your head or on the calculator.
  2. Add the products.
  3. Multiply once by LGD at the end.
  4. For bilateral, repeat with ENE and own PD and subtract.
  5. Eliminate options with the wrong sign: CVA reduces value, DVA increases it.

Common mistakes in Credit Valuation Adjustment (CVA) and DVA

  • Using net expected exposure instead of positive exposure

    Students treat mark-to-market as if negative values offset losses.

    Fix: CVA uses only the positive part, because you owe the full amount if the trade is negative.

  • Forgetting to multiply by LGD

    Students stop after summing EE × PD.

    Fix: Always apply LGD = 1 − recovery. Write it as the final step.

  • Using cumulative default probability for each period

    The CDS or survival data gives cumulative figures.

    Fix: Use the marginal probability: Q(ti-1) − Q(ti).

  • Adding DVA when computing bilateral CVA

    Mixing up the sign of the adjustment.

    Fix: Bilateral CVA = CVA − DVA. The value adjustment is − CVA + DVA.

  • Saying wrong-way risk lowers CVA

    Confusing the independence result with the correlated one.

    Fix: Wrong-way risk means exposure is high when default is likely, so true CVA is higher than the independent estimate.

  • Thinking DVA is a real cash gain you can realise

    Accounting treatment is read as economic profit.

    Fix: DVA gains only crystallise on your own default or restructuring. Basel III excludes it from regulatory capital.

Worked examples

Example 1

A bank has a swap with a corporate. Discounted expected exposure is USD 4 million in year 1 and USD 3 million in year 2. Marginal default probabilities are 2% in year 1 and 3% in year 2. Recovery is 40%. Compute the unilateral CVA.

Show the solution
  1. LGD = 1 − 0.40 = 0.60.
  2. Year 1: 4,000,000 × 0.02 = 80,000.
  3. Year 2: 3,000,000 × 0.03 = 90,000.
  4. Sum = 170,000.
  5. CVA = 0.60 × 170,000 = 102,000.

Answer: CVA = USD 102,000

Example 2

For the same swap, the bank's own marginal default probabilities are 1% in year 1 and 1.5% in year 2. Discounted expected negative exposure is USD 2 million in year 1 and USD 1 million in year 2. The bank's recovery is 40%. The risk-free swap value is USD 500,000 and CVA is USD 102,000. Find bilateral CVA and the adjusted value.

Show the solution
  1. LGD = 0.60.
  2. Year 1: 2,000,000 × 0.01 = 20,000.
  3. Year 2: 1,000,000 × 0.015 = 15,000.
  4. Sum = 35,000; DVA = 0.60 × 35,000 = 21,000.
  5. Bilateral CVA = 102,000 − 21,000 = 81,000.
  6. Adjusted value = 500,000 − 81,000 = 419,000.

Answer: Bilateral CVA = USD 81,000; adjusted value = USD 419,000

Exam tips

  • Check the sign: CVA lowers an asset's value, DVA raises it. Many wrong options flip this.
  • Read whether probabilities are marginal or cumulative before you multiply.
  • Conceptual questions often ask why DVA is controversial or excluded from capital. Mention own-credit-deterioration gains and no hedge.
  • For wrong-way risk, name the direction: exposure rises as counterparty credit worsens, so CVA rises. Right-way risk is the opposite.
  • Know that CVA is hedged with single-name or index CDS, which covers credit spread risk but not the exposure risk.

Practice questions from Counterparty Risk and Beyond

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.

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

What is the difference between CVA and DVA?

CVA is the value lost because your counterparty may default while owing you money. DVA is the value gained because you may default while owing them. Bilateral CVA is CVA minus DVA.

How do you calculate CVA for a swap?

Build the expected positive exposure profile, find marginal default probabilities for each period, multiply them, sum, and multiply by LGD. Use discounted exposures. A swap can have positive exposure at different times, so use the profile, not a single value.

What is wrong-way risk?

It is the risk that exposure to a counterparty increases when its credit quality falls. An example is a bank buying protection from a counterparty highly linked to the reference name. Right-way risk is when exposure falls as default risk rises.

Why is DVA excluded from regulatory capital?

A bank would appear stronger as its own credit worsens, which is perverse. It is also not a loss-absorbing resource in a going concern, so Basel III removes it from capital.