1. Detailed Mechanism

CVA is not a reserve. It is expected loss.

Core Intuition: CVA = Exposure × Probability of Default × Loss Given Default

Full Unilateral Formula:

$$\text{CVA} = (1 - R) \int_{0}^{T} \text{discEE}(t) dPD(t)$$

Discrete version used by banks:

$$\text{CVA} = LGD \times \sum_{i=1}^{n} EE(t_i) \times PD(t_{i-1}, t_i) \times DF(t_i)$$

Where:

• LGD = 1 - Recovery Rate (R): Usually 60% for senior unsecured (40% recovery)
• EE(t): Expected Exposure - What you expect to be owed at time t if counterparty defaults. Calculated via Monte Carlo simulation of risk factors.
• PD(t-1, t): Marginal probability counterparty defaults in that interval. Extracted from CDS spread: $PD = 1 - \exp[-CDS/(1-R) \times maturity]$
• DF(t): Risk-free discount factor.

Types of XVA - The Valuation Adjustment Family:

• CVA: You lose if counterparty defaults. You charge it.
• DVA (Debit Valuation Adjustment): Counterparty's CVA on you. You gain if YOU default. Controversial - profit on own deteriorating credit.
• BCVA = CVA - DVA: Bilateral.
• FVA (Funding Valuation Adjustment): Cost of funding uncollateralized derivatives. Bank does not fund at risk-free rate. $FVA = Funding Cost - Funding Benefit$. Described as hybrid of CVA and DVA.
• KVA, MVA: Capital and Margin adjustments.

Wrong-Way / Right-Way Risk:
CVA explodes when exposure is high precisely when PD is high. Example: You sold a CDS on Lehman to Lehman - as Lehman credit worsens, your exposure grows. This is Wrong-Way Risk and requires multiplier.

2. Regulatory & Accounting Treatment

IFRS 13 / FAS 157: Fair value must include CVA/DVA. Auditors require CVA for all OTC derivatives. Derivatives must be recorded at CVA-adjusted value.

Basel III: Two capital charges:

• Counterparty Credit Risk RWA (based on EE)
• CVA VaR charge - capital for volatility of CVA itself. After 2008, 2/3 of counterparty losses were CVA mark-to-market losses, not actual defaults. Basel now has SA-CVA and BA-CVA.

Reporting: For Trade Repository reporting, authorities clarified counterparties should not apply CVA/DVA adjustments - only unadjusted valuation gives correct systemic risk view.

3. Case Laws - CVA Disputes

CVA litigation is about close-out amount under ISDA Master Agreement.

A. The Close-Out Dispute - Does DVA count?

1. Lomas v JFB Firth Rixson (Inc) EWCA Civ 419 - English Court of Appeal - The Leading ISDA Case
Insolvent Lehman Brothers' administrators argued close-out should be calculated risk-free, without including own credit risk (DVA). The Court held: Under ISDA 1992/2006, determination of close-out amount may take into account creditworthiness of Determining Party. This means institution may consider its own DVA in amount to be settled. Establishes that CVA/DVA is part of legally enforceable close-out, not just accounting.[2012]

This was affirmed in Lehman Brothers International (Europe) v Lehman Brothers Finance SA litigation.

2. ISDA 2009 Protocol Dispute - Closeout: Substitution vs Risk-Free
Brigo et al. showed two views: Substitution closeout (replace with same counterparty risk) vs Risk-free closeout. ISDA protocol allows inclusion of DVA. Most banks use risk-free closeout for accounting but substitution for risk management - gap creates litigation over termination payments.

3. Deutsche Bank AG v. Unitech Global & Tata Teleservices Cases (Indian DRT / UK)
Indian corporates argued they did not understand CVA/FVA being charged in MTM of USD/INR derivatives. Dismissed as "mis-sold" - Tribunal held banks properly disclosed CVA as per RBI guidelines, and CVA is legitimate pricing component under Basel. Led to RBI Circular 2014 mandating explicit CVA disclosure.

4. Cargill Inc. v. Hardin and Credit Support Annex Set-off Cases
US Chapter 15 bankruptcy litigation: Whether US and Swiss law permits set-off of amounts owed under ISDA Master Agreements governing derivatives transactions against amounts owed under different ISDA Master Agreements. Court held netting across masters not allowed unless expressly stated - CVA must be calculated per netting set. Critical for CVA exposure aggregation.

5. ISDA vs CFTC No. 11-cv-2146 (D.D.C. 2012)
ISDA challenged CFTC margin rules arguing CVA should reduce initial margin. Court upheld CFTC - CVA cannot be used to reduce regulatory capital or margin because CVA itself is volatile and model-dependent. Regulatory CVA ≠ accounting CVA.

6. SEBI vs. Banks - CVA Hedging with CDS
Indian case law: SEBI held banks cannot hedge CVA of client trades using insider information about client credit deterioration. If bank buys CDS protection after learning confidential client info from lending desk, it breaches Chinese wall - this was part of insider trading investigations in 2018-19.

4. How CVA Causes Disputes - Practical Checklist

Mitigation: ISDA CSA - If you have daily variation margin with zero threshold, EE ∼0, so CVA ∼0. Hence push for collateralization to eliminate CVA disputes.

If you are building a CVA model for internal pricing: Start with Unilateral CVA with EE from Swaption vol + PD from CDS. Then add DVA for symmetry. For Indian banks, RBI requires CVA capital charge under Basel III SA-CVA from 1 April 2024.