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FRM Exam Part II · Credit Value Adjustment

Bilateral CVA and Debt Value Adjustment (DVA) for FRM Part 2

Updated 11 October 2026 · Fact-checked

Bilateral CVA adjusts a derivative's value for the default risk of both parties. CVA is the cost of the counterparty defaulting on you. DVA is the gain from your own possible default. Bilateral CVA = CVA − DVA, and the adjusted value is the risk-free value minus CVA plus DVA. Compute each from the right exposure and default probability.

Understand Bilateral CVA and Debt Value Adjustment (DVA)

A derivative priced as if both sides always pay is a risk-free value. In reality either side can default. Unilateral CVA only counts the risk that your counterparty defaults while owing you money. This is a cost to you, so it lowers the value of the trade.

Bilateral CVA also counts your own default. If you default while you owe the counterparty money, you do not pay in full. That shortfall is a gain to you, because your liability is worth less. This gain is the debt value adjustment (DVA). The result is: value = risk-free value − CVA + DVA.

CVA depends on the expected positive exposure (what the counterparty owes you), the counterparty's default probability and loss given default. DVA depends on the expected negative exposure (what you owe), your own default probability and your own loss given default. A trade you are owed on drives CVA. A trade you owe on drives DVA.

The first-to-default point matters. Only one party can default first, and the contract ends at that moment. So when you compute CVA you need the counterparty to survive up to the time and you to survive too. Ignoring this double-counts and overstates both CVA and DVA. The exact effect is usually small when default probabilities are low.

DVA is controversial. When your credit spread widens, DVA rises and your reported profit goes up, although your credit has worsened. You cannot easily monetise this gain without defaulting, hedging it is hard, and regulators do not give capital benefit for it. Accounting standards allow it in fair value, but Basel III removes the effect of own-credit gains from regulatory capital. Also, bilateral pricing can make two counterparties disagree on price: each sees the other's CVA as its own DVA only if the inputs match, and they rarely do.

Key formulas to remember

Bilateral value
Value = Risk-free value − CVA + DVA
CVA lowers value. DVA raises value. Bilateral CVA charge = CVA − DVA.
Unilateral CVA (discrete)
CVA = LGD_C × Σ EPE(tᵢ) × DF(tᵢ) × PD(tᵢ₋₁, tᵢ)
EPE is the expected positive exposure. PD is the counterparty's marginal default probability in the period. LGD_C is the counterparty's loss given default.
DVA (discrete)
DVA = LGD_own × Σ ENE(tᵢ) × DF(tᵢ) × PD_own(tᵢ₋₁, tᵢ)
ENE is the expected negative exposure, taken as a positive amount. Uses your own default probability and your own LGD.
First-to-default adjustment
CVA uses PD_C × survival of own; DVA uses PD_own × survival of counterparty
Each default probability is multiplied by the other party's survival probability to that time. This avoids double counting.
Credit triangle (approximation)
Spread ≈ PD (annual hazard) × LGD
Use it to turn a CDS spread into a default probability when the question gives spreads.

How to solve Bilateral CVA and Debt Value Adjustment (DVA) questions

Use this order for any bilateral CVA or DVA question, whether it is numerical or conceptual.

  1. 1Identify who is the counterparty and who is the institution. State whose view the question takes.
  2. 2Decide which exposure feeds which adjustment: positive exposure to CVA, negative exposure to DVA.
  3. 3Get the default probabilities. If given spreads, use spread ÷ LGD as the hazard rate, then PD = 1 − e^(−hazard × t).
  4. 4Check whether the question asks for first-to-default. If so, multiply each PD by the other party's survival probability.
  5. 5Compute each period: LGD × exposure × discount factor × PD, then sum over periods.
  6. 6Combine: value = risk-free value − CVA + DVA. The bilateral CVA charge is CVA − DVA.
  7. 7Interpret the sign and size. Say what a widening of your own spread does to DVA and reported profit.

Quickest way: Sign and direction check

When to use it: Use this on conceptual MCQs or when options differ mainly by direction.

  1. Counterparty credit worsens: CVA up, trade value down.
  2. Your own credit worsens: DVA up, trade value up, reported profit up.
  3. If you only owe money (a liability), CVA is zero and only DVA remains.
  4. If you are only owed money, DVA is zero and only CVA remains.
  5. First-to-default adjustment always reduces both CVA and DVA compared with the unadjusted figures.
  6. For numbers, work one period at a time and sum. Do not estimate the whole life in one step.

Common mistakes in Bilateral CVA and Debt Value Adjustment (DVA)

  • Adding DVA to CVA as if both are losses.

    Both are called adjustments, so students assume the same sign.

    Fix: CVA is a cost and DVA is a benefit. Bilateral CVA charge = CVA − DVA.

  • Using the counterparty's default probability in the DVA calculation.

    Students copy the CVA formula and forget the roles reverse.

    Fix: For DVA use your own default probability, your own LGD and expected negative exposure.

  • Thinking higher own credit risk is bad for reported value.

    Intuition says weaker credit must reduce value.

    Fix: A weaker own credit raises DVA, which raises the fair value of your net position. This is exactly why DVA is criticised.

  • Ignoring first-to-default.

    Textbook examples often show simple unilateral formulas.

    Fix: When asked, multiply each PD by the other party's survival probability. Each adjustment becomes smaller.

  • Treating DVA as a hedgeable, capital-supporting gain.

    It appears in profit and loss, so it looks real.

    Fix: You can only realise it if you default or buy back your own debt. Basel III excludes own-credit gains from regulatory capital.

  • Using a single LGD for both sides.

    Questions often give one recovery rate, and students apply it blindly.

    Fix: Read the question. Use the counterparty's LGD for CVA and your own for DVA. If only one is given, state that it applies to both.

Worked examples

Example 1

A bank has a one-year swap with a counterparty. Over the year, the expected positive exposure is USD 4 million and the expected negative exposure is USD 2 million (treat both as constant for the single period, discount factor 1). The counterparty's one-year default probability is 3% with LGD 60%. The bank's own one-year default probability is 1% with LGD 60%. Ignore first-to-default. The risk-free value is USD 0.50 million. Find the bilateral value.

Show the solution
  1. CVA = 60% × 4,000,000 × 3% = 0.6 × 4,000,000 × 0.03 = USD 72,000.
  2. DVA = 60% × 2,000,000 × 1% = 0.6 × 2,000,000 × 0.01 = USD 12,000.
  3. Bilateral CVA charge = 72,000 − 12,000 = USD 60,000.
  4. Value = 500,000 − 72,000 + 12,000 = USD 440,000.

Answer: CVA = USD 72,000, DVA = USD 12,000, and the bilateral value is USD 440,000 (USD 0.44 million).

Example 2

Same trade as above, but apply first-to-default for the single period, using each party's one-year survival probability of the other. Compute CVA and DVA.

Show the solution
  1. Counterparty survival = 1 − 0.03 = 0.97. Bank survival = 1 − 0.01 = 0.99.
  2. CVA = 0.6 × 4,000,000 × 0.03 × 0.99 = 72,000 × 0.99 = USD 71,280.
  3. DVA = 0.6 × 2,000,000 × 0.01 × 0.97 = 12,000 × 0.97 = USD 11,640.
  4. Bilateral CVA charge = 71,280 − 11,640 = USD 59,640.

Answer: CVA = USD 71,280, DVA = USD 11,640, bilateral charge = USD 59,640. Both are slightly smaller than the unadjusted figures.

Exam tips

  • Always write the sign first: CVA reduces value, DVA increases it. Many wrong options only flip a sign.
  • Watch for the phrase first-to-default. It signals multiplying by the other party's survival probability.
  • Conceptual questions often ask why DVA is problematic: it rewards deteriorating own credit, is hard to hedge and gets no regulatory capital recognition.
  • When spreads are given, convert with spread ÷ LGD before computing PD. Check whether the question uses annual or cumulative probabilities.
  • If an option says a party with only liabilities has CVA, reject it. Only DVA applies there.

Practice questions from Credit Value Adjustment

Bilateral CVA and Debt Value Adjustment (DVA): frequently asked questions

What is the difference between CVA and DVA?

CVA is the adjustment for the risk that your counterparty defaults while owing you money, and it lowers the trade value. DVA is the adjustment for your own default risk, and it raises the trade value because your liability is worth less. Bilateral CVA combines them as CVA − DVA.

What is first-to-default in bilateral CVA?

Only one party can default first, and the contract ends then. So the counterparty's default only matters if you have survived, and your default only matters if the counterparty has survived. You multiply each default probability by the other party's survival probability.

Why is DVA controversial?

A fall in your own credit quality raises DVA and increases reported profit. You cannot easily realise or hedge that gain. Basel III removes own-credit gains from regulatory capital, and counterparties rarely agree on each other's DVA.

Can DVA be hedged?

Not cleanly. You would need to sell protection on yourself, which is not practical. Some firms use proxies such as sector CDS, but these leave basis risk.