FRM Exam Part II · Credit Risk Management

Counterparty Credit Risk and Exposure Measures for FRM Part II

Updated 11 October 2026 · Fact-checked

Counterparty credit risk is the risk that a derivative counterparty defaults while you are owed money. You measure it with exposure profiles: EE is the average future positive value, PFE is a high percentile of it, and EPE is the time average of EE. Netting and collateral reduce exposure. CVA prices the expected loss.

Understand Counterparty Credit Risk and Exposure Measures

Counterparty credit risk (CCR) arises when a trade has a value that can change sign. A loan has a fixed amount at risk. A swap does not. If the swap is worth +₹10 crore to you and the counterparty defaults, you lose. If it is worth negative, you still owe the amount. Your exposure is therefore the positive part of the value: max(V, 0).

Because future value is uncertain, you describe exposure with a distribution at each future date. Expected exposure (EE) is the mean of the positive exposure at a date. Potential future exposure (PFE) is a high percentile (for example 95% or 97.5%) of that same distribution. EE is used for pricing and capital. PFE is used for limits. Expected positive exposure (EPE) is the average of EE over time. Effective EE is forced to be non-decreasing over the first year, which reflects short-dated trades being rolled over. Effective EPE is the average of effective EE over that first year.

Netting lets you offset positive and negative trades with one counterparty under an enforceable master agreement (such as an ISDA). Exposure becomes max(sum of values, 0) instead of the sum of the positive values. Collateral reduces exposure further. Exposure becomes the uncollateralised amount, and risk remains over the margin period of risk, the time between the last margin call and close-out.

Credit valuation adjustment (CVA) is the market value of counterparty credit risk. In its simple unilateral form it is the sum over time of discounted EE × the counterparty's marginal default probability × LGD. DVA (debit valuation adjustment) is the mirror item for your own default risk. It is a gain to you, because your own default would reduce what you owe. Bilateral CVA = unilateral CVA − DVA, so the bilateral figure is lower than the unilateral figure.

Wrong-way risk arises when your exposure to the counterparty rises as the counterparty's default probability rises. It is seen from the point of view of the party that is owed money. Examples are a derivative whose underlying is the counterparty's own shares or debt, such as you buying a put on the counterparty's shares, or buying CDS protection from a counterparty that is highly correlated with the reference entity (or that writes protection on itself). In each case the trade is worth most to you just when the counterparty is weakest. Standard CVA assumes exposure and default are independent, so it understates the loss. Right-way risk is the opposite.

Key formulas to remember

Exposure: Exposure = max(V, 0); V is the value of the trade or netted portfolio to you at the future date.
Expected exposure: EE(t) = E[max(V(t), 0)]; Average of positive values only. Negative values count as zero.
Potential future exposure: PFE(t) = the α-percentile of max(V(t), 0); Usually 95% to 99%. It is a limit-setting measure and is not an average.
Expected positive exposure: EPE = (1 ÷ T) × ∫ EE(t) dt, or the average of EE over the dates; A time average. Effective EPE uses a non-decreasing EE profile over the first year.
Unilateral CVA: CVA ≈ LGD × Σ [EE*(tᵢ) × PD(tᵢ₋₁, tᵢ)], with EE* discounted; LGD = 1 − recovery. PD is the marginal default probability in each period. Assumes independence of exposure and default.
Marginal PD from a constant hazard rate: PD(t₁, t₂) = e^(−λt₁) − e^(−λt₂); λ is the hazard rate. Approximately λ ≈ spread ÷ LGD.
Net exposure: Net exposure = max(Σ Vᵢ, 0) ≤ Σ max(Vᵢ, 0); Netting never increases exposure.
Collateralised exposure: Exposure = max(V − C, 0); C is collateral held (after haircuts). Risk remains from movement over the margin period of risk.

How to solve Counterparty Credit Risk and Exposure Measures questions

Use the same sequence for any question on exposure, mitigants or CVA.

1Identify what is asked: a point exposure, a profile statistic (EE, PFE, EPE), a mitigant effect, or CVA.
2Set the exposure as the positive part of value. Replace any negative value with zero before averaging or taking percentiles.
3Apply netting first if there is an enforceable agreement. Sum the trade values in the netting set, then take max(sum, 0).
4Apply collateral next. Subtract collateral held after haircuts and floor at zero. Think about the margin period of risk.
5For CVA, list the dates, the EE (discounted), the marginal PD and LGD. Multiply for each period and add up.
6Check for wrong-way or right-way risk. If exposure and default are linked, say that the independence-based number is understated or overstated.
7Sanity check: PFE ≥ EE, net ≤ gross, and collateralised ≤ uncollateralised.

Quickest way: Floor, net, subtract, then multiply

When to use it: Numerical questions with a short table of values or a list of trades and a collateral amount.

Floor each scenario value at zero before averaging (EE) or ranking (PFE).
For netting sets, add signed values first, then floor once.
Subtract collateral last and floor again.
For CVA, compute LGD × EE × marginal PD for each period and sum. Do not forget discounting if given.
For multiple-choice conceptual items, remember: PFE is a percentile, EPE is a time average, netting reduces exposure, and wrong-way risk raises CVA.

Common mistakes in Counterparty Credit Risk and Exposure Measures

Averaging signed values to get EE.
You treat EE like the expected value of the trade.
Fix: Floor at zero first. EE is the mean of max(V, 0), so it is never negative.
Treating PFE as the average of the worst cases.
It gets confused with expected shortfall.
Fix: PFE is a single percentile of the exposure distribution. It is not a tail average.
Netting each trade then adding the positives.
You floor too early.
Fix: Sum all trades in the netting set first and floor once. Flooring early gives gross exposure.
Using cumulative PD instead of marginal PD in CVA.
Both are shown in the table and look similar.
Fix: Each period's EE is paired with the probability of default in that period only: the difference of cumulative PDs.
Assuming full collateral means zero risk.
You ignore the delay between default, the last call and close-out.
Fix: Residual exposure remains from market moves in the margin period of risk, plus thresholds, minimum transfer amounts and haircuts.
Saying wrong-way risk lowers CVA.
You mix up the direction of the link.
Fix: Wrong-way risk means higher exposure when default is more likely, so CVA from the independence formula is too low.

Worked examples

Example 1

A bank has two trades with one counterparty under an enforceable netting agreement. In a future scenario, trade A is worth +$8 million and trade B is worth −$5 million. Five equally likely scenarios give the netted portfolio values (in $ million): +3, −2, +6, −4, +1. Find the netted exposure in the first scenario and the EE at that date across all five scenarios.

Show the solution

Netted value in the first scenario = 8 + (−5) = +3. Exposure = max(3, 0) = $3 million.
Floor the five netted values: 3, 0, 6, 0, 1.
Sum = 3 + 0 + 6 + 0 + 1 = 10.
EE = 10 ÷ 5 = $2 million.
Gross check for the first scenario: gross exposure would be 8 + 0 = $8 million, so netting cut exposure from 8 to 3.

Answer: Netted exposure in the first scenario is $3 million, and EE across the five scenarios is $2 million.

Example 2

A counterparty has marginal default probabilities of 2% in year 1 and 3% in year 2. LGD is 60%. Discounted EE is $10 million in year 1 and $14 million in year 2. Using the unilateral formula with independence, calculate CVA.

Show the solution

CVA = LGD × Σ (discounted EE × marginal PD).
Year 1: 10 million × 0.02 = $0.20 million.
Year 2: 14 million × 0.03 = $0.42 million.
Sum = 0.20 + 0.42 = $0.62 million.
Multiply by LGD: 0.62 × 0.60 = $0.372 million.

Answer: CVA = $0.372 million, about $372,000. If the counterparty shows wrong-way risk, the true CVA would be higher.

Exam tips

Know the definitions cold: EE is a mean of positive values, PFE is a percentile, EPE is a time average. Many questions are just this distinction.
In numerical items, floor at zero before you do anything else, and floor once for a netting set.
For CVA, use marginal PDs and LGD = 1 − recovery. Check whether EE is already discounted.
Wrong-way risk questions test direction: more exposure when default is likelier, CVA understated by independence. General wrong-way (macro link) differs from specific wrong-way (legal or structural link).
Netting needs legal enforceability. If a scenario says the netting agreement may not hold in insolvency, assume exposure is gross.

Practice questions from Credit Risk Management

Counterparty Credit Risk and Exposure Measures: frequently asked questions

What is the difference between expected exposure and potential future exposure?

EE is the average of the positive exposure at a future date, and it feeds CVA and capital. PFE is a high percentile of the same distribution, such as 97.5%. It shows a plausible worst case and is used to set limits.

What is CVA and how is it calculated?

CVA is the market value of counterparty default risk on a derivative portfolio. In the simple version you sum, over each time period, LGD × discounted EE × marginal default probability. It assumes exposure and default are independent.

How do netting and collateral reduce counterparty risk?

Netting offsets gains and losses across trades with one counterparty, so exposure is max(sum of values, 0). Collateral covers the positive exposure with assets you hold. Some risk remains from price moves during the margin period of risk.

What is wrong-way risk in FRM?

It is the risk that your exposure to a counterparty grows just as its credit quality worsens. Examples include buying protection from a bank whose default would coincide with the reference entity's stress. It makes CVA higher than the independence model suggests.