FRM Exam Part II · Counterparty Risk and Beyond

XVA: FVA, KVA and MVA Explained

Updated 11 October 2026 · Fact-checked

XVA is the family of valuation adjustments added to a derivative's risk-free value. CVA covers counterparty default, DVA your own default, FVA funding costs, KVA the cost of regulatory capital, and MVA the cost of funding initial margin. To solve questions, identify the cost source, then size it as exposure × rate × time, discounted.

Understand Other Valuation Adjustments and Funding Costs (XVA)

A derivative's risk-free value ignores real-world frictions. A dealer must also deal with counterparty default, funding the hedges, holding capital and posting margin. XVA puts a price on each of these. The sum of the adjustments is subtracted from (or added to) the risk-free value to get the price the dealer actually charges.

CVA is the expected loss from counterparty default. DVA is the mirror image: the gain from your own default, because you would not pay in full. FVA is the cost or benefit of funding the uncollateralised part of a trade. If the dealer is owed money on a trade, it must fund that position at its own funding spread, so FVA is a cost. If it owes money, it receives a funding benefit.

KVA is the cost of holding regulatory capital over the life of the trade. It is the expected capital held in each period, multiplied by the bank's hurdle rate (the return shareholders demand), discounted. MVA is the cost of funding initial margin posted to a CCP or under bilateral rules. Initial margin is typically not returned until the trade ends, so its funding cost is a real charge.

Why it matters: hedging a client trade with a collateralised trade in the market creates a mismatch. The client trade may be uncollateralised while the hedge needs variation margin. The dealer funds the gap. That funding cost is the core of FVA.

A key debate is overlap. FVA and DVA both relate to the dealer's own credit spread, so adding both can double count the benefit. Many practitioners therefore price DVA and FVA carefully, or exclude DVA from the price. Know that this debate exists. Know too that the exposure measures behind XVA are expected exposure profiles, often from Monte Carlo simulation.

Key formulas to remember

Price with adjustments: Price = Risk-free value − CVA + DVA − FVA − KVA − MVA; Signs show a cost to the dealer. Some costs can be benefits, such as FVA on a liability position. Check the sign convention in the question.
CVA (discrete): CVA = LGD × Σ [EE(ti) × PD(ti-1, ti) × DF(ti)]; EE is the discounted or undiscounted expected positive exposure. Use one convention consistently. LGD = 1 − recovery rate.
FVA (simple): FVA ≈ Σ [EE(ti) × s_f × Δt × DF(ti)]; s_f is the funding spread over the risk-free rate. Use expected positive exposure for the funding cost and expected negative exposure for the funding benefit.
KVA (simple): KVA ≈ Σ [Expected capital(ti) × hurdle rate × Δt × DF(ti)]; The hurdle rate is the cost of capital. Some versions use the excess over the risk-free rate, so read the wording.
MVA (simple): MVA ≈ Σ [Expected IM(ti) × funding spread × Δt × DF(ti)]; IM is initial margin. The spread is the cost of funding the margin, net of any interest earned on it.
Approximate CVA, flat exposure: CVA ≈ EE × LGD × PD; A shortcut for a single period or constant exposure and hazard rate.

How to solve Other Valuation Adjustments and Funding Costs (XVA) questions

Use this method for any XVA question, whether it asks for a number, a sign or a concept.

1Name the adjustment being asked about: CVA, DVA, FVA, KVA or MVA. Match it to its cost source: counterparty default, own default, funding, capital or initial margin.
2Identify the exposure that drives it: expected positive exposure for costs, expected negative exposure for benefits, expected capital for KVA, expected initial margin for MVA.
3Pick the rate: LGD × default probability for CVA, funding spread for FVA and MVA, hurdle rate for KVA.
4Multiply exposure × rate × period length, then apply the discount factor if the question gives one.
5Sum across periods if there is more than one.
6Apply the sign: costs reduce the price, benefits increase it. Then check the direction against intuition.
7Interpret: say who bears the cost, and flag any overlap such as FVA and DVA, or whether collateral reduces the figure.

Quickest way: Match cost to rate, then multiply

When to use it: Use when a question gives one or two periods of exposure and a spread or rate, and asks for an adjustment or ranks adjustments.

Underline the cost source in the stem: funding, capital or margin.
Pick the matching rate: funding spread, hurdle rate or margin funding spread.
Compute exposure × rate × time. Use the given discount factor only if provided.
Eliminate options with the wrong sign or an unmatched rate, such as using LGD for FVA.
For concept questions, remember: collateral cuts CVA and FVA, initial margin creates MVA, capital creates KVA.

Common mistakes in Other Valuation Adjustments and Funding Costs (XVA)

Using LGD and default probability to compute FVA.
CVA is the first adjustment learned, so its formula becomes the default.
Fix: FVA depends on the funding spread, not on counterparty default. Use exposure × funding spread × time.
Treating FVA as always a cost.
Students see 'funding cost' and forget the other side of the trade.
Fix: Positive exposure creates a funding cost. Negative exposure creates a funding benefit. Net the two as the question directs.
Adding DVA and FVA benefits without comment.
Both are shown as separate items in a table.
Fix: Both relate to the dealer's own credit spread, so benefits can double count. Note the overlap in any interpretation question.
Confusing MVA with KVA.
Both involve something held against a trade.
Fix: KVA is the cost of regulatory capital, charged at the hurdle rate. MVA is the cost of funding initial margin posted to others, charged at a funding spread.
Forgetting to discount or to use the period length.
Rushing to multiply exposure by the rate.
Fix: Include Δt for the period and the discount factor whenever the question supplies them.
Assuming collateral removes all XVA.
Collateral does cut CVA, so students overgeneralise.
Fix: Variation margin cuts exposure but not to zero because of the margin period of risk. Initial margin removes credit risk but adds MVA.

Worked examples

Example 1

A dealer has an uncollateralised derivative with a client. The expected positive exposure is USD 10 million for each of the next two years. The dealer's funding spread is 1.5% per year. The discount factors are 0.97 for year 1 and 0.94 for year 2. Estimate the FVA cost. Choose: A) USD 0.147 million, B) USD 0.286 million, C) USD 0.300 million, D) USD 0.450 million.

Show the solution

The funding cost comes from funding the positive exposure at the funding spread.
Year 1: 10 × 0.015 × 1 × 0.97 = 0.1455.
Year 2: 10 × 0.015 × 1 × 0.94 = 0.1410.
Total = 0.1455 + 0.1410 = 0.2865, about 0.286 million.

Answer: B) about USD 0.286 million (0.2865). It is a cost, so it lowers the price.

Example 2

A one-year uncollateralised swap has a flat expected positive exposure of USD 8 million. The counterparty's one-year default probability is 2.5% and the recovery rate is 40%. Using the single-period approximation with no discounting, estimate the CVA. Choose: A) USD 0.08 million, B) USD 0.12 million, C) USD 0.20 million, D) USD 0.48 million.

Show the solution

LGD = 1 − recovery = 1 − 0.40 = 0.60.
CVA ≈ EE × LGD × PD.
CVA ≈ 8 × 0.60 × 0.025.
8 × 0.60 = 4.8. Then 4.8 × 0.025 = 0.12.

Answer: B) USD 0.12 million. This is the expected loss from counterparty default, deducted from the risk-free value.

Exam tips

Read the stem for the cost source. 'Funding' points to FVA, 'initial margin' to MVA, 'regulatory capital' to KVA.
Check the sign. Many options differ only in sign, so decide whether the dealer pays or receives.
Expect interpretation questions on the FVA and DVA overlap and on why collateral does not remove all costs.
Use only the discount factors and spreads given. Do not invent extra adjustments to the arithmetic.
Know which adjustments move with the dealer's own spread: DVA and FVA. CVA moves with the counterparty's spread.

Practice questions from Counterparty Risk and Beyond

Other Valuation Adjustments and Funding Costs (XVA): frequently asked questions

What is the difference between CVA and FVA?

CVA prices the expected loss if the counterparty defaults. FVA prices the cost of funding the trade or its hedges at the dealer's own funding spread. CVA uses LGD and default probability. FVA uses exposure and the funding spread.

What is KVA in simple terms?

KVA is the cost of holding regulatory capital against a trade for its whole life. You estimate expected capital over time, multiply by the hurdle rate and discount. It is a charge to the client price.

Why does initial margin create MVA?

Initial margin is posted and not available for other use until the trade ends. The dealer must fund it, so the funding spread on the expected margin is a cost. That cost is MVA.

Is there double counting between DVA and FVA?

There can be. Both benefit from a wider dealer credit spread, so counting both fully may overstate the benefit. Practitioners therefore treat the overlap carefully, and this is a common discussion point in exam questions.