Credit value adjustment (CVA) is the market-standard valuation adjustment that accounts for the risk of counterparty default on an OTC derivative. It represents the difference between the risk-free portfolio value and the portfolio value accounting for the possibility that the counterparty may default before all contractual obligations are fulfilled. CVA is the oldest and most established member of the xVA family, and it has become a key component of both accounting (IFRS 13, FASB 157) and regulatory capital (Basel III) frameworks.
The standard unilateral CVA (UCVA) formula under independence of exposure and default is:
UCVA(t) = -LGD * sum_{i=1}^{m} EPE(t, t_i) * PD(t_{i-1}, t_i)
where LGD is the loss given default, EPE is the discounted expected positive exposure, and PD is the marginal default probability over each interval. This formula can also be written as a continuous integral involving the counterparty’s hazard rate and a risky discount factor. An approximate “spread” version is UCVA ~ -average_EPE * credit_spread, which separates the market risk component (exposure) from the credit component.
CVA is computed using market-implied (risk-neutral) parameters in line with the exit-price concept required by accounting standards. This means credit spreads rather than historical default probabilities should be used. CVA can be hedged dynamically using CDS indices and other market instruments, and is typically managed by a dedicated CVA desk (or more broadly, an xVA desk) that prices, owns, and hedges the counterparty risk transferred from originating trading desks.
A distinctive feature of CVA relative to other xVA terms is that it is contingent on a default event. If the counterparty never defaults, the CVA cost is never realised. This makes CVA “the least real valuation adjustment” in the sense that funding, collateral, and capital costs are ongoing production costs visible even absent default.
Key Details
- The direct CVA simulation (simulating random default times) converges roughly 36 times faster than the path-wise approach (simulating entire exposure profiles) for the same number of portfolio valuations, due to autocorrelation in successive path-wise valuations.
- CVA is a portfolio-level (specifically counterparty/netting-set-level) calculation: it should be computed incrementally, capturing netting effects across all trades with a given counterparty.
- CVA can be expressed as a running spread by dividing by a duration/annuity, though this ignores the recursive “CVA of the CVA” effect.
- Two opposing approaches exist: actuarial CVA (reserve based on historical default probabilities) vs. risk-neutral CVA (exit price based on credit spreads). The risk-neutral approach is now dominant.
Textbook References
The xVA Challenge (Gregory, 2020)
- Section 3.1.6 (pp. 50—51): CVA as the actual price of counterparty risk, replacing binary credit limits with a continuous pricing metric. CVA is additive across counterparties but does not distinguish concentrated portfolios.
- Section 3.1.7 (pp. 51—52): Actuarial vs. risk-neutral CVA. The risk-neutral approach has become dominant due to accounting standards (FAS 157, IFRS 13), Basel III rules, and market practice. Risk-neutral default probabilities are derived from credit spreads.
- Section 5.2.7 (pp. 92—93): CVA is “the least real” xVA because it depends on a default event that may never occur; an analogy is drawn with a short out-of-the-money option position.
- Section 17.2.2 (pp. 487—490): The direct CVA formula UCVA(t) = -E[I(tau ⇐ T) V(t,tau)^+ LGD] (Eq. 17.1) and the path-wise discrete approximation UCVA ~ -LGD sum EPE(t,t_i) PD(t_{i-1},t_i) (Eq. 17.3). The direct simulation approach converges much faster than the path-wise method.
- Section 17.2.3 (pp. 492—493): CVA as a running spread: UCVA ~ -average_EPE * spread (Eq. 17.4), useful for intuitive understanding of CVA drivers.
- Section 5.3.3 (pp. 95—97): IFRS 13 and FASB 157 require inclusion of counterparty credit risk (CVA) and own credit risk (DVA) in fair value measurement, using market-implied risk premiums.
- Section 17.2.6 (pp. 495—497): LGD in CVA. Eq. 17.5 distinguishes LGD_actual (expected recovery at default) from LGD_mkt (used to calibrate default probabilities from CDS). When LGD_actual = LGD_mkt, the LGD terms cancel to first order; changing LGD from 60% to 50% changes CVA by less than 2%. Different LGDs are justified for project finance (75% average recovery) or different-seniority exposures.
- Section 17.3.3 (pp. 500—502): bilateral CVA formula (Eq. 17.7—17.8). BCVA = CVA + DVA, with the “first-to-default” effect conditioning each party’s loss on the other’s survival. The simple approximation BCVA ~ -EPE x (Spread_C - Spread_P).
- Section 17.4.1 (pp. 506—509): Incremental CVA (Eq. 17.11—17.12) uses incremental EPE; never worse than standalone CVA due to netting. Marginal CVA (Section 17.4.2, pp. 509—510) allocates total netting-set CVA to transactions for accounting.
- Section 17.5 (pp. 510—514): Impact of margin on CVA. Even zero-threshold, two-way margining produces material CVA due to the 10-day MPoR. Initial margin drives CVA toward zero. Collateralised DVA is even more controversial.
- Section 17.6 (pp. 514—527): Wrong-way risk in CVA. Intensity, structural, parametric, and jump approaches compared. The structural copula approach produces much stronger WWR than the intensity approach at equal correlation. Specific WWR in credit derivatives: at 60% correlation, CVA on a bought CDS is ~50 bps (one-fifth of the 250 bps premium). Collateralisation is of limited help against jump-type WWR.