What is Funding Valuation Adjustment (FVA) and how does it relate to CVA/DVA?

Funding Valuation Adjustment (FVA) captures the cost or benefit of funding uncollateralized derivative positions at a rate different from the risk-free rate. It reflects the reality that banks borrow at SOFR + spread, not at the theoretical risk-free rate, and this funding cost should be priced into derivatives.

The Core Idea

When a bank has a positive MTM derivative (the counterparty owes the bank), the bank effectively needs to fund that receivable. If the trade is uncollateralized, the bank cannot use the counterparty's collateral to fund the position — it must borrow in the market.

Conversely, when the bank has a negative MTM (the bank owes the counterparty) and the trade is uncollateralized, the bank has use of cash it would otherwise have posted as collateral — a funding benefit.

FVA Formula

FVA = FCA + FBA

Where:

• FCA (Funding Cost Adjustment) = Cost of funding positive exposures

FCA = −integral of [EE(t) x s_F(t) x D(t)] dt

• FBA (Funding Benefit Adjustment) = Benefit from negative exposures

FBA = +integral of [ENE(t) x s_F(t) x D(t)] dt

EE(t) = Expected Exposure, ENE(t) = Expected Negative Exposure, s_F(t) = funding spread.

Worked Example

Briarwood Capital has an uncollateralized 3-year cross-currency swap with a corporate client. The bank's funding spread is 85 bps.

Net FVA = −$314,500 + $127,500 = −$187,000

The swap has a net funding cost of $187,000 that should be charged to the client.

FVA vs. DVA: The Double-Counting Debate

This is a major theoretical controversy:

• DVA says the bank benefits from its own default risk (lower survival probability reduces the PV of its obligations).
• FBA says the bank benefits from using funding from negative-MTM positions.
• Critics argue these capture similar effects and including both overstates the benefit.

In practice, most banks now include FVA but have reduced or eliminated DVA from P&L recognition (though DVA may still appear for regulatory purposes).

Exam Tip: Know that FVA is controversial because risk-neutral pricing theory says funding costs should not affect derivative valuation (Modigliani-Miller). But in practice, banks are not frictionless and funding costs are real. The FRM exam tests both perspectives.

For more XVA content, check our FRM Part II question bank.