What is CVA and how does DVA work as a bilateral credit adjustment?

CVA and DVA are adjustments to the mark-to-market value of derivative positions that account for the possibility that either counterparty might default.

Credit Valuation Adjustment (CVA):

CVA represents the market value of counterparty credit risk — it's the expected loss due to the counterparty defaulting on its obligations.

CVA ≈ Σ [EE(tᵢ) × PD(tᵢ₋₁, tᵢ) × LGD × DF(tᵢ)]

Where:

• EE(t) = Expected Exposure at time t (positive replacement cost)
• PD(t₁,t₂) = Probability of default between t₁ and t₂
• LGD = Loss Given Default (1 - Recovery Rate)
• DF(t) = Discount factor

Intuition: CVA is the price of a contingent CDS — you're buying protection against the counterparty defaulting when they owe you money.

Debit Valuation Adjustment (DVA):

DVA is the mirror image — it represents the value of your own default risk to the counterparty.

DVA ≈ Σ [NEE(tᵢ) × PD_own(tᵢ₋₁, tᵢ) × LGD_own × DF(tᵢ)]

Where NEE is the Negative Expected Exposure (when you owe the counterparty).

The bilateral valuation:

Adjusted Value = Risk-Free Value - CVA + DVA

• Subtract CVA (cost of counterparty's default risk — bad for you)
• Add DVA (benefit of your own default risk — you might not have to pay)

Why DVA is controversial:

1. Counterintuitive P&L: When your own credit quality deteriorates (e.g., credit spread widens), DVA increases, creating a gain on your P&L. Your bank is becoming riskier but booking profits.
2. 2011 example: Several major banks reported billions in "DVA gains" during periods of credit stress — this made their results look better precisely when they were in trouble.
3. Regulatory skepticism: Basel III excludes DVA gains from regulatory capital (CET1) — banks cannot count this as "real" capital.
4. Hedgeability: CVA can be hedged by buying CDS on the counterparty. DVA would require selling CDS on yourself — which is problematic.

Numerical example:

Granite Bank has a 5-year interest rate swap with Apex Corp:

• Risk-free MTM: +$8M (Apex owes Granite)
• CVA (Apex default risk): $1.2M
• DVA (Granite's own default risk): $0.4M

Bilateral adjusted value = $8M - $1.2M + $0.4M = $7.2M

From Apex's perspective: -$8M + $1.2M - $0.4M = -$7.2M (consistent — both see the same adjusted value)

Exam tip: FRM Part II tests CVA calculation, the bilateral framework (CVA + DVA), and the regulatory treatment of DVA. Know why DVA creates counterintuitive P&L and why regulators exclude it from capital.

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