CVA and XVA Explained: Pricing the True Cost of a Derivatives Trade

CVA — Credit Valuation Adjustment — is the adjustment made to the fair value of a derivatives portfolio to reflect the risk that the counterparty might default before the contract matures. It converts a risk-free derivative valuation into a 'credit-adjusted' value: what the portfolio is actually worth, given the possibility of counterparty default.

Why CVA exists

Before the 2008 financial crisis, most banks priced OTC derivatives as if their counterparties could never default. The crisis demonstrated how wrong this assumption was: Lehman Brothers' default crystallised large losses for counterparties who had assumed their trades would perform until maturity.

Post-crisis, regulators required CVA to be calculated, reported, and — under Basel III — charged with capital. CVA is now a standard part of derivative pricing for uncollateralised or partially collateralised trades.

What CVA captures

CVA represents the expected loss on a derivatives portfolio from counterparty default. It depends on three inputs: the Probability of Default of the counterparty (derived from their CDS spreads or internal credit assessments); the Loss Given Default (1 minus the expected recovery rate); and the Expected Positive Exposure (how much the bank is owed at the time of potential default).

The key insight is that CVA is only relevant when the bank is owed money: if the bank owes the counterparty money and the counterparty defaults, the bank's obligation simply disappears. CVA captures only the asymmetric, one-sided exposure.

The XVA family

CVA is the original and most important XVA, but the family has grown. DVA (Debit Valuation Adjustment) reflects the bank's own credit risk. FVA (Funding Valuation Adjustment) reflects the cost of funding uncollateralised derivatives positions. MVA (Margin Valuation Adjustment) reflects the cost of posting initial margin. KVA (Capital Valuation Adjustment) reflects the cost of holding regulatory capital against the trade.

Each XVA represents a real economic cost that must be recovered in pricing. How each is calculated and managed, and how XVA desks coordinate across the markets business, are covered in Market Mechanics — the complete plain-English guide to how a bank's markets business works.