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FRM Part 2 · Worked study notes

Counterparty Credit Risk and CVA Intuition

Counterparty credit risk concerns replacement loss when a derivative counterparty defaults while the contract has positive value to you. CVA reduces a default-free value for expected counterparty loss. Exposure can change with market conditions and need not equal notional.

The method at a glance

  • 01Positive exposure

    How it works: Consider replacement value after legally effective netting and collateral.

    Watch for: Counting a negative contract value as an asset exposure to that counterparty.

  • 02CVA

    How it works: Combine discounted expected exposure, LGD and interval default probabilities.

    Watch for: Multiplying cumulative PD by exposure repeatedly across time buckets.

  • 03Wrong-way risk

    How it works: Exposure rises when counterparty credit quality deteriorates.

    Watch for: Assuming exposure and default are independent in all cases.

Original worked example

A one-period unilateral CVA estimate

Expected positive exposure is 2 million, one-period PD is 3%, LGD is 60% and the discount factor is 0.98. Assume exposure independent of default, fixed recovery and no own-default adjustment.

  1. STEP 1

    Undiscounted expected counterparty loss = 2,000,000 × 0.03 × 0.60 = 36,000.

  2. STEP 2

    Discount the loss: 36,000 × 0.98 = 35,280.

  3. STEP 3

    Subtract this CVA from the default-free value under the simplified unilateral convention.

CVA ≈ 35,280. This is a valuation adjustment, not the derivative notional or a regulatory capital charge.

Illustrative assumptions and calculations for learning. Not observed market data or an official exam item.

Apply the method and check its limits

Before you start: Positive replacement value, discounting, default probabilities and LGD.

Calculate exposure after an enforceable netting set

Current exposure = max(net replacement value - eligible collateral, 0), in the simplified case

Two trades worth +3 million and -2 million with the same counterparty have net value +1 million if they are in an enforceable netting set. With 0.4 million usable collateral, current exposure is 0.6 million. Without enforceable netting, the positive trade cannot automatically be offset by the negative one. Current exposure also differs from future expected exposure.

Use interval default probabilities in a time grid

Unilateral CVA ≈ LGD × Σ DFᵢ × EEᵢ × ΔPDᵢ

EE is expected positive exposure at the relevant future interval, DF discounts the loss, and ΔPD is unconditional default probability during that interval. With cumulative PDs of 2% at year one and 5% at year two, the increments are 2% and 3%. Using 2% and 5% would count first-year default probability twice. Exposure-default independence is a simplifying assumption, not a universal property.

Collateral reduces exposure, but timing remains

Thresholds, minimum transfer amounts, collateral disputes and the margin period of risk leave residual exposure. A default can occur while prices move before replacement or closeout. Netting is useful only within enforceable agreements and eligible sets. A one-period independence formula is a teaching approximation; wrong-way risk requires a joint exposure/default treatment.

Work through the topic

Move from derivative values to net exposure and a simplified CVA calculation. Track collateral, interval default probabilities and wrong-way risk explicitly.

Calculate exposure within the correct netting set

A derivative can have positive or negative value as market conditions change. Counterparty exposure concerns the positive replacement value that may be lost if the counterparty defaults, subject to the applicable arrangements. A negative value is generally an obligation of the institution, not a negative credit loss that can freely cancel exposure to an unrelated party.

Consider two trades with one counterparty, valued at +3 million and -2 million. Without recognized netting, the sum of positive trade values is 3 million. With an enforceable close-out netting arrangement covering both trades, the net value is +1 million before collateral and other adjustments. The economic offset is relevant only within the valid agreement; moving the negative trade to another counterparty changes the exposure.

If 0.7 million of eligible collateral is available against that netting set under the assumed terms, a simplified current unsecured exposure is max(1.0 - 0.7, 0) = 0.3 million. Thresholds, minimum transfer amounts, valuation disputes and the period needed to close out can leave exposure. A current collateral balance is not a complete description of future credit risk.

Original current-exposure reconciliation, millions

No recognized netting
Calculation: max(3, 0) + max(-2, 0)
Exposure: 3.0
Enforceable netting
Calculation: max(3 - 2, 0)
Exposure: 1.0
Netting plus eligible collateral
Calculation: max(1.0 - 0.7, 0)
Exposure: 0.3

Use interval default probability once per interval

A simplified unilateral CVA estimates discounted expected counterparty credit losses. Assume deterministic LGD, supplied expected positive exposures, discount factors and default probabilities suitable for the valuation purpose, with exposure-default dependence ignored. Sum LGD × expected exposure × discount factor × probability of default within each interval. These assumptions make the arithmetic transparent but omit important features of a production valuation.

For an original three-interval example, cumulative default probabilities are 2%, 5% and 9%. The interval probabilities are therefore 2%, 3% and 4%, not 2%, 5% and 9%. Expected exposures in millions are 1.0, 1.4 and 1.1; discount factors are 0.99, 0.96 and 0.93; LGD is 60%. The interval contributions are 11,880, 24,192 and 24,552, totaling CVA of 60,624.

Using cumulative probabilities in every row would count earlier default probability repeatedly. Likewise, mixing real-world default forecasts with a market valuation setup without explanation creates a conceptual inconsistency. Identify the probability measure, exposure convention and interval timing. The example uses supplied inputs and does not infer market-implied probabilities from credit spreads.

Original simplified unilateral CVA, currency units

1
Inputs: EE × discount × interval PD × LGD: 1,000,000 × 0.99 × 0.02 × 0.60
Contribution: 11,880
2
Inputs: EE × discount × interval PD × LGD: 1,400,000 × 0.96 × 0.03 × 0.60
Contribution: 24,192
3
Inputs: EE × discount × interval PD × LGD: 1,100,000 × 0.93 × 0.04 × 0.60
Contribution: 24,552
Total
Inputs: EE × discount × interval PD × LGD: Sum of interval contributions
Contribution: 60,624

Challenge exposure-default dependence and close-out timing

Wrong-way risk arises when exposure tends to increase as the counterparty becomes more likely to default. For example, a hedge linked to a commodity can become valuable to the institution precisely when a commodity-sensitive counterparty weakens. Treating exposure and default as independent can miss this adverse connection. The contractual direction and counterparty business matter; the instrument’s name alone does not determine the sign of dependence.

Collateral reduces specified exposures but introduces timing and funding questions. Markets can move between the last successful margin exchange and close-out. A dispute can delay a transfer. Collateral can fall in value or become difficult to realize. Model those mechanisms according to the agreement rather than assuming daily margining makes exposure identically zero.

Keep CVA separate from funding and other valuation adjustments. A bilateral treatment may consider the institution’s own default as well, while a unilateral example considers counterparty default only. Adding adjustments requires consistent conventions to avoid double counting. For risk management, inspect the exposure profile and its drivers as well as the single present-value adjustment.

Is expected exposure the same as potential future exposure?

No. Expected exposure averages positive exposure at a future time under the chosen model. Potential future exposure commonly refers to a specified exposure quantile. State the date, confidence level and netting/collateral assumptions when reporting the latter.

Can a swap with zero initial value have counterparty risk?

Yes. Future market movements can make it valuable to one party. Zero value at inception does not imply zero future positive exposure, and collateral arrangements may leave timing or threshold gaps.

Try a changed assumption

Under exposure-default independence, with 2 million expected exposure in both periods, LGD 60%, discount factors 1 and cumulative PDs 2% then 5%, what is CVA?

Show answer and reasoning

2,000,000 × 0.60 × (0.02 + 0.03) = 60,000. Summing the cumulative probabilities would incorrectly produce 84,000.

Original learning check. No email or account needed.

Does a collateral agreement make CVA zero?

Not necessarily. Exposure can remain through thresholds, timing gaps, disputes, collateral value changes or unenforceable netting.

Sources and scope

Links checked 2026-10-10. GARP establishes exam scope; the technical references support the methods identified below. These are selected study notes and original examples, not complete curriculum coverage or official exam questions.

Prepared by MiloPrep editorial team. MiloPrep is independent of GARP. References do not imply endorsement or independent review of these notes.