Valuation Adjustments: CVA, DVA, FVA
Valuation Adjustments: CVA, DVA, FVA
Valuation adjustments (XVAs) modify derivative fair values to reflect counterparty credit risk and funding costs. CVA captures the risk that your counterparty defaults, DVA reflects your own default risk, and FVA accounts for funding costs. Understanding these adjustments is essential for accurate pricing and P/L attribution.
Definition and Key Concepts
XVA Family
| Adjustment | Full Name | What It Captures |
|---|---|---|
| CVA | Credit Valuation Adjustment | Counterparty default risk |
| DVA | Debt Valuation Adjustment | Own default risk |
| FVA | Funding Valuation Adjustment | Funding costs/benefits |
| ColVA | Collateral Valuation Adjustment | Collateral rate differences |
| KVA | Capital Valuation Adjustment | Cost of regulatory capital |
| MVA | Margin Valuation Adjustment | Cost of initial margin |
CVA Fundamentals
CVA definition: The expected loss from counterparty default, calculated as:
CVA = Σ (Probability of Default × Expected Exposure × Loss Given Default)
Key inputs:
- Credit spreads (imply default probability)
- Expected positive exposure (EPE) over time
- Recovery rate (typically 40% for senior unsecured)
DVA Fundamentals
DVA definition: The benefit from your own potential default, a symmetric concept to CVA from the counterparty's perspective.
DVA = Σ (Own Probability of Default × Expected Negative Exposure × Own LGD)
Controversy: DVA gains occur when your credit deteriorates—benefiting from increased default probability is counterintuitive and creates P/L volatility.
FVA Fundamentals
FVA definition: The cost or benefit of funding uncollateralized derivative positions.
FVA = Σ (Funding Spread × Expected Funding Requirement × Time)
Components:
- Funding benefit adjustment (FBA): Benefit when receiving funding
- Funding cost adjustment (FCA): Cost when providing funding
How It Works in Practice
CVA Calculation
Simple CVA formula: CVA = (1 - R) × ∫ EE(t) × dPD(t)
Where:
- R = Recovery rate
- EE(t) = Expected exposure at time t
- PD(t) = Cumulative probability of default to time t
Practical implementation:
| Step | Activity |
|---|---|
| 1 | Simulate market scenarios (Monte Carlo) |
| 2 | Value portfolio under each scenario at each time point |
| 3 | Calculate expected positive exposure profile |
| 4 | Apply counterparty default probability from credit curve |
| 5 | Integrate over time, applying loss given default |
Exposure Profiles
Key exposure metrics:
| Metric | Definition |
|---|---|
| Expected Exposure (EE) | Average positive exposure at time t |
| Potential Future Exposure (PFE) | 97.5th percentile exposure |
| Expected Positive Exposure (EPE) | Time-weighted average of EE |
| Peak Exposure | Maximum PFE across time |
Example exposure profile (5-year IRS):
| Time | EE | PFE (97.5%) |
|---|---|---|
| 6 months | $2.5M | $8.0M |
| 1 year | $4.0M | $12.0M |
| 2 years | $5.5M | $16.0M |
| 3 years | $5.0M | $15.0M |
| 4 years | $3.5M | $11.0M |
| 5 years | $0 | $0 |
Peak exposure typically occurs mid-life for swaps.
Worked Example
Trade details:
- Product: 5-year USD interest rate swap
- Notional: $100 million
- Direction: Bank receives fixed
- Counterparty: BBB-rated corporate
- Collateral: Uncollateralized
Counterparty credit data:
- 5-year CDS spread: 150 bps
- Recovery rate: 40%
Step 1: Calculate probability of default Using CDS spread: Annual hazard rate ≈ Spread / (1 - R) = 1.50% / 0.60 = 2.5% 5-year cumulative PD ≈ 1 - e^(-0.025 × 5) ≈ 11.75%
Step 2: Calculate expected exposure From Monte Carlo simulation: Average EPE over 5 years = $4.5 million
Step 3: Calculate CVA CVA = LGD × EPE × Effective PD Contribution CVA ≈ 60% × $4,500,000 × Σ(marginal PD × discount factor) CVA ≈ $320,000
Interpretation: The bank should charge the counterparty approximately $320,000 (or 32 bps upfront) to compensate for credit risk on this trade.
FVA Calculation
Additional inputs:
- Bank funding spread: SOFR + 80 bps
- Risk-free rate: SOFR
- Expected funding requirement: $3 million average
FVA calculation: FVA = Funding Spread × Expected Funding × Duration FVA ≈ 0.80% × $3,000,000 × 4.5 years FVA ≈ $108,000
Total XVA charge: CVA + FVA = $320,000 + $108,000 = $428,000 (or 43 bps upfront)
Impact of Collateral
| Collateral Status | CVA | FVA | Total XVA |
|---|---|---|---|
| Uncollateralized | $320,000 | $108,000 | $428,000 |
| Daily VM | $50,000 | $20,000 | $70,000 |
| Daily VM + IM | $15,000 | $5,000 | $20,000 |
Collateralization dramatically reduces XVA charges.
Risks, Limitations, and Tradeoffs
P/L Volatility
XVA creates earnings volatility from:
| Source | Trigger | P/L Impact |
|---|---|---|
| Credit spread moves | Counterparty spread widens | CVA loss |
| Own credit moves | Own spread widens | DVA gain |
| Funding spread moves | Funding costs increase | FVA loss |
| Exposure changes | Market moves | All XVAs change |
DVA Controversy
| Argument For DVA | Argument Against DVA |
|---|---|
| Symmetric to counterparty's CVA | Gains from deteriorating credit |
| Required by accounting standards | Not realizable in liquidation |
| Reflects true liability value | Creates perverse incentives |
Many institutions exclude DVA from performance metrics despite accounting recognition.
Model Risk
| Factor | Uncertainty |
|---|---|
| Credit spreads | May not reflect true default probability |
| Recovery rates | Highly variable in actual defaults |
| Exposure simulation | Model assumptions affect results |
| Wrong-way risk | Correlation between exposure and default |
Wrong-Way Risk
Definition: Exposure increases when counterparty credit deteriorates.
Example:
- Bank sells put option to counterparty
- Market crashes, option goes ITM
- Counterparty likely to default when owing money
Wrong-way risk requires scenario analysis beyond standard CVA models.
Common Pitfalls
| Pitfall | Description | Prevention |
|---|---|---|
| Ignoring netting | CVA calculated trade-by-trade | Use netting set level calculation |
| Static exposure | Exposure assumed constant | Use dynamic simulation |
| Missing collateral effect | CVA ignores margin | Include CSA terms in exposure |
| Double counting | FVA overlaps with CVA | Consistent framework |
Accounting and Regulatory Treatment
Accounting (IFRS/US GAAP)
| Standard | CVA | DVA | FVA |
|---|---|---|---|
| IFRS 13 | Required | Required (OCI option) | Permitted |
| ASC 820 | Required | Required | Permitted |
DVA through OCI: IFRS 9 allows DVA changes on own credit to flow through Other Comprehensive Income rather than P/L.
Regulatory Capital
| Treatment | Requirement |
|---|---|
| CVA risk charge | SA-CVA or BA-CVA under Basel III |
| DVA | Not recognized for capital |
| FVA | Not in regulatory framework |
Banks must hold capital for CVA volatility risk.
Checklist and Next Steps
CVA implementation checklist:
- Establish exposure simulation infrastructure
- Source counterparty credit spreads
- Define netting sets aligned with ISDA relationships
- Include CSA terms in exposure calculation
- Implement wrong-way risk adjustments
- Set up daily CVA calculation and attribution
- Establish governance for model validation
XVA pricing checklist:
- Calculate CVA for new trades
- Include FVA based on funding requirements
- Consider MVA for cleared trades
- Build XVA into trade pricing
- Attribute P/L to XVA components daily
- Report XVA to risk management
Related articles:
- For portfolio optimization, see Compression and Portfolio Tear-Ups
- For accounting treatment, see Accounting Treatment for Hedging Swaps