Credit Valuation Adjustment (CVA): Formula, Example, and XVA Overview

When a bank enters an OTC derivative — such as an interest rate swap or currency swap — the risk-free valuation assumes both counterparties will honor every cash flow. In reality, the counterparty might default before all payments are exchanged. Credit valuation adjustment (CVA) is the risk-neutral pricing adjustment that accounts for this possibility, reducing the derivative’s value by the market price of counterparty credit risk. The 2008 financial crisis made CVA a front-office concern: the Basel Committee on Banking Supervision noted that roughly two-thirds of counterparty credit losses during the crisis were CVA losses — mark-to-market declines driven by widening credit spreads — rather than actual defaults. Today, CVA is both an accounting requirement under IFRS 13 and ASC 820 and a regulatory capital charge under Basel III.

What is Credit Valuation Adjustment (CVA)?

CVA represents the difference between a derivative’s risk-free value and its true value after accounting for the counterparty’s possible default. In formal terms:

CVA is not a one-time charge calculated at trade inception. It is a mark-to-market adjustment that changes every day as market conditions evolve. At major banks, dedicated CVA desks actively manage and hedge CVA exposure across the entire derivatives portfolio.

Unilateral vs bilateral CVA: Unilateral CVA assumes only the counterparty can default. Bilateral CVA also accounts for the bank’s own default risk through a debit valuation adjustment (DVA). This article presents the unilateral CVA framework; DVA and other valuation adjustments are covered in the XVA overview below.

The CVA Formula

The standard unilateral CVA formula sums the discounted expected losses across discrete time intervals over the derivative’s life:

Where:

• LGD (Loss Given Default) — the fraction of exposure lost if the counterparty defaults, equal to 1 − Recovery Rate. Typically 60% for senior unsecured OTC derivatives
• EE(t_i) (Expected Exposure) — the average positive mark-to-market value of the derivative at time t_i, computed from Monte Carlo simulation across thousands of market scenarios
• PD(t_i-1, t_i) (Marginal Probability of Default) — the probability the counterparty defaults during the interval [t_i-1, t_i], conditional on surviving to t_i-1
• DF(t_i) (Discount Factor) — the present value factor at time t_i, derived from the OIS (Overnight Index Swap) zero-coupon curve

Under a constant hazard rate, the marginal default probability for each interval can be expressed as:

The hazard rate h can be approximated from observable market data as h ≈ CDS Spread / LGD. This is an approximation that assumes a flat hazard rate, matched tenor, and negligible liquidity and risk premia effects — but it provides a practical starting point for CVA estimation.

CVA Input Stack

Each component of the CVA formula comes from a distinct analytical discipline. The table below maps each input to its source methodology:

The shape of the expected exposure (EE) profile varies significantly by derivative type. Interest rate swaps exhibit a characteristic hump-shaped EE profile — exposure rises as rates diverge from inception values (diffusion effect) then declines as the remaining cash flows decrease (amortization effect), typically peaking around one-third to one-half of the swap’s tenor. Currency swaps, by contrast, have exposure that increases toward maturity because the large principal re-exchange at maturity creates significant credit risk.

Netting, Collateral, and Margin Period of Risk

Three factors dramatically affect the EE profile — and therefore CVA — before any formula calculation begins:

• Netting agreements reduce EE by offsetting positive and negative mark-to-market values across all trades with the same counterparty under an ISDA Master Agreement
• Collateral (CSA) further compresses exposure by requiring periodic margin posting — a fully collateralized netting set has dramatically lower CVA than an uncollateralized trade
• Margin period of risk (MPOR) — collateral is not received instantaneously. The MPOR (typically 10 business days for bilateral trades, 5 for centrally cleared) represents the window during which exposure can build before a default is resolved

How to Calculate Credit Valuation Adjustment (Step-by-Step)

Spread shock sensitivity: If Ford’s CDS spread widens from 150 bps to 250 bps (credit deterioration), the hazard rate increases from 0.025 to approximately 0.042, and marginal PDs roughly increase by 65%. CVA would rise from ~$82,400 to approximately $133,000 — a ~$51,000 mark-to-market loss for Goldman’s CVA desk, even though no default has occurred.

Collateralized vs uncollateralized: If this same swap were under a Credit Support Annex (CSA) with daily margin posting and a 10-day margin period of risk, the EE profile would be dramatically compressed — peak EE might drop from $2.0M to approximately $0.3M. The resulting CVA would fall to roughly $12,000, illustrating why collateral agreements are the most effective CVA mitigant in practice.

CVA vs DVA vs FVA vs MVA vs KVA (XVA Overview)

CVA was the first valuation adjustment to gain widespread adoption, but banks now compute a family of adjustments — collectively called XVAs — that determine the true economic price of an OTC derivative:

DVA is the most controversial XVA. It implies that a bank’s own deteriorating creditworthiness creates accounting gains — since DVA increases when the bank’s CDS spread widens. Some regulators exclude DVA from capital calculations for this reason, though it is permitted under IFRS 13 and ASC 820.

FVA emerged as a major concern post-2008 as bank funding costs increased. It captures the real-world cost dealers face when funding the cash flows of uncollateralized positions. Together, these XVAs determine the “all-in” price a dealer must charge to trade at zero economic profit.

CVA vs Credit Risk

The fundamental difference is that CVA is computed under risk-neutral probabilities and flows through fair-value P&L, while loan loss provisions use real-world (statistical) probabilities and follow expected credit loss accounting. This makes CVA more volatile — it can swing significantly with CDS spread movements even when the counterparty’s fundamental credit quality remains unchanged.

CVA and Basel III Capital Charge

Before Basel III, CVA risk was not separately capitalized. The Basel Committee on Banking Supervision (BCBS) noted in 2011 that roughly two-thirds of counterparty credit losses during the 2008 crisis were CVA-related mark-to-market losses rather than actual defaults. This gap prompted the introduction of a dedicated CVA capital charge to capture the risk of mark-to-market CVA losses driven by credit spread movements.

The final Basel III framework provides two approaches for calculating the CVA capital charge:

• SA-CVA (Standardised Approach) — a formulaic calculation based on regulatory credit spread sensitivities, available to banks subject to supervisory approval
• BA-CVA (Basic Approach) — a simplified reduced-sensitivity method designed for banks with smaller derivative portfolios

The advanced internal-model approach for CVA, which permitted banks to use proprietary models, was removed in the final Basel III reforms (BCBS d424, 2017) — standardizing the CVA capital framework across institutions.

Common Mistakes

1. Confusing CVA with expected loss. CVA is a market-priced (risk-neutral) adjustment, not an actuarial reserve. It uses risk-neutral PDs derived from CDS spreads and will typically exceed the actuarial expected loss because market-implied PDs embed a credit risk premium. The two serve different purposes: CVA is for fair-value pricing, expected loss is for reserving.

2. Ignoring wrong-way risk. Standard CVA models assume exposure and default probability are independent. In practice, they can be positively correlated — for example, buying FX options from a counterparty whose currency is weakening, or receiving floating rate from a counterparty whose credit deteriorates as rates rise. Wrong-way risk can cause actual CVA losses to far exceed model estimates. See the discussion in our counterparty credit risk guide.

3. Treating CVA as a one-time calculation. CVA is a dynamic mark-to-market quantity that changes every day as exposure profiles evolve, credit spreads move, and interest rates shift. Banks must recalculate CVA daily and manage the resulting P&L volatility.

4. Assuming netting eliminates CVA entirely. Netting reduces exposure — and therefore CVA — by offsetting positive and negative mark-to-market values across trades with the same counterparty. But netting cannot reduce net exposure below zero: if the net portfolio value is positive, CVA still applies to the remaining exposure.

5. Using the wrong PD type. Risk-neutral PDs (from CDS spreads) are required for CVA pricing under fair-value accounting. Real-world PDs (from rating agencies or historical data) are appropriate for loan loss provisioning and economic capital. Mixing these inputs produces systematically incorrect results.

6. Using cumulative PD instead of marginal PD. Each interval in the CVA summation requires the marginal (conditional) default probability for that specific period — not the cumulative probability of default from time zero. The marginal PD accounts for the counterparty having survived to the start of each interval.

7. Using a single EPE number instead of the full EE term structure. CVA requires the expected exposure at each time step to capture how the exposure profile shape interacts with the time-weighted default probabilities. Replacing the full EE term structure with a single expected positive exposure (EPE) number loses this interaction and can materially misstate CVA.

Limitations of CVA

1. Model dependence. CVA requires Monte Carlo simulation of exposure profiles, calibration of credit curves, and assumptions about recovery rates and correlations. Different modeling choices — simulation paths, time grid granularity, volatility assumptions — can produce significantly different CVA estimates for the same derivative portfolio.

2. Wrong-way risk is hard to model. Capturing the correlation between exposure and default probability requires joint simulation frameworks that are computationally expensive and statistically difficult to calibrate from the limited data available on actual defaults.

3. CDS liquidity constraints. CVA relies on CDS spreads for market-implied default probabilities, but many counterparties — particularly corporates and sovereigns — do not have actively traded CDS contracts. For these names, banks must use proxy spreads mapped by rating, sector, and geography, introducing additional estimation error.

4. Regulatory vs accounting divergence. The Basel III CVA capital charge and the accounting CVA under IFRS 13 / ASC 820 may use different inputs, netting assumptions, and modeling methodologies. This can produce conflicting results — a trade that appears well-hedged for accounting purposes may still carry significant regulatory CVA capital.