When a bank quotes a price on a derivative to a client, the rate it offers is not simply the mid-market swap rate plus a bid/offer spread. The desk must also account for a series of costs and risks that exist because derivatives are not traded in a frictionless world. These adjustments — collectively called XVA (valuation adjustments) — can add several basis points to the client-facing rate and, for large long-dated trades, can make a significant difference to whether the trade is economically attractive to the bank.
CVA: Credit Valuation Adjustment
CVA is the adjustment for the risk that the counterparty to a derivative will default before the contract matures. When a bank enters a swap with a corporate client, there is some probability — however small — that the client will default when the swap has a positive value for the bank (i.e., the client owes the bank money). If the client defaults at that point, the bank may recover only a fraction of what it is owed.
CVA is calculated as the expected cost of this counterparty default, discounted to present value. Formally:
CVA ≈ (1 − Recovery Rate) × ∫ Probability of Default(t) × Expected Positive Exposure(t) × Discount Factor(t) dt
The three key inputs are: the probability of the counterparty defaulting at each future date (derived from their CDS spread or internal credit model), the expected positive exposure (EPE) at each date — how much the bank is owed on average across all market scenarios — and the loss given default (1 minus recovery rate). CVA is always a cost to the bank (a deduction from the trade's value) because the bank bears the risk of being owed money when the counterparty fails.
Banks typically run a dedicated CVA desk that prices CVA on new trades and hedges the resulting credit risk — buying CDS protection on the client to offset the default exposure. The CVA charge is passed through to the originating trading desk as a cost of doing business, and ultimately to the client through the all-in rate.
DVA: Debit Valuation Adjustment
DVA is the mirror of CVA — it is the bank's own credit risk from the counterparty's perspective. If the bank defaults when the swap has a positive value for the client (the bank owes the client money), the client may not recover in full. This is a benefit to the bank: it can potentially walk away from its liabilities at less than par.
DVA is therefore a gain in the bank's P&L. When a bank's credit spreads widen (its perceived default probability rises), its DVA increases — generating a P&L gain on its derivatives book. This is deeply counterintuitive and has been the source of significant controversy: banks booking profits because they have become more likely to default. In practice, DVA is real but difficult to hedge (you would need to buy back your own debt or buy protection on yourself), and most banks do not hedge it. Some regulators and accounting standards are moving to reduce its prominence.
FVA: Funding Valuation Adjustment
FVA is the cost of funding uncollateralised derivatives. When a bank enters a swap with a client that has no CSA (or a one-way CSA where only the client must post collateral), the bank may owe variation margin to its CCP on the hedging swap while receiving no collateral from the client. The bank must fund this margin from its own treasury at its internal funding rate — which is typically higher than the risk-free rate.
The funding benefit or cost of this asymmetry is the FVA. If the bank pays SONIA + 30bp to fund its balance sheet but receives only SONIA on its collateral at the CCP, the 30bp spread is an ongoing cost embedded in the trade. FVA is charged on new trades at inception and amortises over the life of the swap as the funding requirement changes with the trade's mark-to-market value.
FVA was controversial when it was first widely adopted post-2008. Some academics argued it represented double-counting with DVA. In practice, virtually all major derivatives dealers now charge FVA because the funding costs are real and the trade-level pricing must reflect them.
MVA: Margin Valuation Adjustment
MVA is the cost of the initial margin (IM) required for cleared or bilateral derivatives under the BCBS/IOSCO uncleared margin rules (UMR). Initial margin is locked up as collateral at the CCP or a segregated custodian — it cannot be rehypothecated by the bank. Funding this locked-up collateral has a cost: the bank must hold liquid assets (cash or government bonds) to post as IM, and those assets have an opportunity cost.
MVA became increasingly important after the September 2016 start of UMR Phase 1 and the subsequent roll-out to smaller entities. For long-dated bilateral swaps now subject to mandatory IM exchange, MVA can be several basis points per annum — a material cost that the bank must recover through its client pricing.
KVA: Capital Valuation Adjustment
KVA is the cost of the regulatory capital a bank must hold against a derivative position. Under Basel III/IV, banks must hold a minimum level of capital (Common Equity Tier 1) against the risk-weighted assets (RWAs) of their derivatives books. This capital is expensive — the bank's shareholders require a return on it. If a derivative generates £1 million of RWA and the bank must hold 15% of that as CET1 capital (£150,000), and its cost of equity is 10%, the capital cost is £15,000 per year.
KVA converts this annual capital cost into an upfront charge embedded in the derivative price. It is the most opaque and most debated XVA — the cost of capital depends on internal capital allocation models, and different banks price KVA very differently. Banks with higher internal hurdle rates (return-on-equity targets) will price derivatives more expensively on a KVA basis.
Practical Impact on Trade Pricing
For a vanilla five-year interest rate swap with a well-rated, fully collateralised (CSA) counterparty: XVA charges might be minimal — perhaps 0.5–1bp total. For a long-dated, bilateral (uncleared) swap with a corporate that has no CSA, the XVA burden could be 5–20bp or more. This can make certain trades uneconomic with certain counterparties, pushing clients to either clear through a CCP (eliminating most XVA) or accept worse all-in pricing.