FRM Exam Part II · Credit Risk

Credit Exposure and Counterparty Credit Risk 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. Exposure is the positive part of the contract value, max(V, 0). You measure it with EE, EPE and PFE, reduce it with netting and collateral, and price it as CVA. Wrong-way risk raises exposure when default probability is high.

Understand Credit Exposure and Counterparty Credit Risk

A loan has a fixed exposure: the amount lent. A derivative does not. Its value changes with markets and can be positive or negative for you. You only lose if the counterparty defaults while the contract is worth a positive amount to you. So credit exposure is the larger of the contract value and zero: max(V, 0). If the value is negative, you owe money and your exposure is zero.

Because future values are uncertain, you describe exposure with a profile over time. Expected exposure (EE) at a date is the average of the positive values at that date. Expected positive exposure (EPE) is the time-average of EE over a period, often one year. Potential future exposure (PFE) is a high percentile, such as 95% or 99%, of the exposure distribution at a date. Peak exposure is the maximum of PFE over the life. EE and EPE are averages used for pricing and capital. PFE is a tail measure used for credit limits.

Netting lets you combine all trades with one counterparty under a legally enforceable master agreement, so that at default you owe or are owed one net amount. Netted exposure is max(ΣV, 0), which is never greater than Σmax(V, 0). Without enforceability, a liquidator can cherry-pick: keep the trades good for them and walk away from the rest. Collateral reduces exposure further. Under a credit support agreement, the party that is out of the money posts collateral. Exposure is then what could build up during the margin period of risk, the time between the last margin call received and the close-out of the position.

Credit valuation adjustment (CVA) is the market value of counterparty credit risk. In its simple unilateral form, CVA ≈ LGD × Σ EE(ti) × PD(ti-1, ti), using risk-neutral default probabilities and discounted exposures. DVA is the mirror image: the value to you of your own default risk. Wrong-way risk arises when exposure to a counterparty is high just when its default probability is high, for example buying protection from a bank that is exposed to the same assets. It makes CVA larger than a model that assumes independence. Right-way risk is the opposite.

Key formulas to remember

Credit exposure of one trade: Exposure = max(V, 0); V is the mark-to-market value to you. Negative value means zero exposure.
Expected exposure and EPE: EE(t) = E[max(V(t), 0)]; EPE = average of EE(t) over the period; EPE is a time average of EE. It is not a percentile.
Potential future exposure: PFE(t) = the q-th percentile of max(V(t), 0), e.g. q = 95% or 99%; Used for limits. It is always at or above EE at the same date.
Netted exposure: Netted = max(V1 + V2 + ... + Vn, 0) ≤ Σ max(Vi, 0); Holds only if netting is legally enforceable in the relevant jurisdiction.
Net-to-gross ratio: NGR = Netted exposure ÷ Gross exposure; A lower ratio means a bigger netting benefit.
Unilateral CVA (discrete): CVA ≈ LGD × Σ [discounted EE(ti) × marginal PD(ti-1, ti)]; Assumes exposure and default are independent. LGD = 1 − recovery rate.
Bilateral adjustment: Bilateral CVA = CVA − DVA; DVA gains when your own credit worsens, which is controversial.
Collateralised exposure: Exposure ≈ max(V(t) − C, 0), where C is collateral held at the time of default; The key driver is the margin period of risk, which sets how far V can move before close-out.

How to solve Credit Exposure and Counterparty Credit Risk questions

Use this order for any counterparty exposure question. It stops you mixing up measures.

1Identify what is asked: exposure profile (EE, EPE, PFE), mitigation effect (netting, collateral) or valuation (CVA, DVA).
2Compute exposure per trade as max(V, 0) at each scenario or date. Never average negative values into EE.
3For netting, sum the values within the netting set first, then take max(sum, 0). Do this per scenario.
4For collateral, subtract collateral held from the netted value, then floor at zero. Think about the margin period of risk and any threshold or minimum transfer amount.
5For PFE, read off the stated percentile of the exposure distribution. For EPE, average the EE values over time.
6For CVA, multiply LGD by the sum of discounted EE times the marginal default probability in each interval.
7Check the wrong-way link: does exposure rise when the counterparty weakens? If so, the independence-based answer understates CVA.
8Sanity check: netted ≤ gross, PFE ≥ EE, and exposure is never negative.

Quickest way: Floor, net, then weight

When to use it: Use it for numeric questions with a small table of values or a short exposure and PD schedule.

Floor each trade value at zero, but only after you have netted within any netting set.
Compare the two totals: gross sums the floored trade values, netted floors the sum.
For CVA, compute LGD × EE × PD for each period, then add. Use the given discount factors.
For concept questions, eliminate options that say netting increases exposure, that PFE is an average, or that wrong-way risk lowers CVA.

Common mistakes in Credit Exposure and Counterparty Credit Risk

Averaging negative values when computing EE.
You treat EE like an expected mark-to-market value.
Fix: Apply max(V, 0) in each scenario first, then average.
Calling EPE a percentile or PFE an average.
The names sound similar and both describe future exposure.
Fix: EPE is a time-average of EE. PFE is a high percentile at a date. Use EPE for pricing and capital, PFE for limits.
Applying netting across counterparties or without a legal agreement.
You assume offsetting trades always cancel.
Fix: Netting works only within a legally enforceable netting set with one counterparty, such as under an ISDA Master Agreement.
Taking the maximum before summing in a netting set.
You apply the floor trade by trade out of habit.
Fix: Sum the values in the set, then floor once. Netted exposure never exceeds gross.
Using real-world default probabilities in CVA.
Historical PDs feel more natural.
Fix: CVA is a market price, so use risk-neutral PDs implied by CDS spreads or bond spreads.
Saying collateral removes all exposure.
You ignore the gap between default and close-out.
Fix: Residual exposure remains from the margin period of risk, thresholds, minimum transfer amounts and collateral value changes.

Worked examples

Example 1

A bank has three trades with one counterparty under an enforceable netting agreement. Mark-to-market values to the bank are +USD 12 million, −USD 5 million and +USD 3 million. Compute gross exposure, netted exposure and the net-to-gross ratio. Then find exposure if the bank holds USD 4 million of collateral.

Show the solution

Gross exposure = max(12, 0) + max(−5, 0) + max(3, 0) = 12 + 0 + 3 = USD 15 million.
Netted value = 12 − 5 + 3 = USD 10 million, so netted exposure = USD 10 million.
Net-to-gross ratio = 10 ÷ 15 = 0.667, or about 66.7%.
With collateral of USD 4 million, exposure = max(10 − 4, 0) = USD 6 million.

Answer: Gross USD 15 million; netted USD 10 million; NGR about 66.7%; exposure after collateral USD 6 million.

Example 2

A bank estimates expected exposure to a counterparty at the end of years 1, 2 and 3 of USD 8 million, USD 10 million and USD 6 million (already discounted). Marginal risk-neutral default probabilities for years 1, 2 and 3 are 2%, 3% and 4%. Recovery rate is 40%. Estimate unilateral CVA, assuming exposure and default are independent.

Show the solution

LGD = 1 − 0.40 = 0.60.
Year 1: 8 × 0.02 = 0.16.
Year 2: 10 × 0.03 = 0.30.
Year 3: 6 × 0.04 = 0.24.
Sum = 0.16 + 0.30 + 0.24 = 0.70.
CVA = 0.60 × 0.70 = USD 0.42 million.

Answer: CVA ≈ USD 0.42 million (USD 4,20,000). If wrong-way risk were present, the true CVA would be higher.

Exam tips

Questions often ask which measure suits which purpose: EPE for CVA and capital, PFE for limits, so memorise that split.
In netting questions, sum first and floor once. Expect distractors that floor each trade and call it netted.
For wrong-way risk, remember the direction: it raises exposure at default and raises CVA. Specific wrong-way risk comes from the trade's legal or economic link to the counterparty, general wrong-way risk from macro conditions.
Look for the word 'enforceable'. If netting is not enforceable, use gross exposure.
In CVA questions, check whether PDs are marginal or cumulative, and whether EE is already discounted.

Practice questions from Credit Risk

Credit Exposure and Counterparty Credit Risk: frequently asked questions

What is the difference between EPE and PFE?

EPE is the time-average of expected exposure, where exposure is the positive part of the contract value. PFE is a high percentile, such as 97.5% or 99%, of the exposure distribution at a future date. EPE feeds pricing and capital. PFE feeds credit limits.

How does netting reduce counterparty exposure?

Under an enforceable master agreement, all trades with a counterparty are combined into one net claim at default. Gains on some trades offset losses on others, so netted exposure max(ΣV, 0) is at most the sum of positive trade values. The benefit is larger when trades have values of opposite sign.

What is wrong-way risk?

It is the risk that exposure to a counterparty is high when its probability of default is also high. A bank selling you credit protection on assets tied to its own health is a classic example. It makes losses worse than a model assuming independence would show.

How is CVA calculated in the exam?

Use LGD times the sum, over time intervals, of discounted expected exposure and marginal default probability. Use risk-neutral probabilities. If the question mentions bilateral CVA, subtract DVA.