1. What is CVA?

Formal Definition:

CVA represents the difference between a derivative's risk-free value and its true value after accounting for the counterparty's possible default

Adjusted Value = Risk-Free Value − CVA

CVA is defined in Article 381 CRR as: an adjustment to the mid-market valuation of the portfolio of transactions with a counterparty reflects the current market value of the credit risk of the counterparty to the institution[which]

CVA is the market value of counterparty Credit Risk on derivative portfolios. Under Basel III, banks must hold capital against CVA risk, reflecting the potential for mark-to-market losses due to deterioration in counterparty creditworthiness

In plain English: If you have a Rs 100 cr in-the-money swap with a BBB counterparty, you will not realize Rs 100 cr. You have to discount it because there is a chance he defaults. That discount is CVA.

Accounting: CVA is both an accounting requirement under IFRS 13 and ASC 820 and a regulatory capital charge under Basel III

The Formula

$$CVA = LGD \times \sum_{i=1}^{T} EE_i \times PD_i \times DF_i$$

Where:

• $LGD$ = Loss Given Default (1 - Recovery)
• $EE_i$ = Expected Exposure at time i
• $PD_i$ = Probability of Default in interval
• $DF_i$ = Discount Factor

CVA is the risk-neutral discounted expected value of the potential loss

Simplified: CVA = Present value of Expected Loss on a trade due to default by counterparty

XVA Family

• CVA: Your loss if counterparty defaults (you bear their risk) - always reduces value
• DVA: Your gain if YOU default (counterparty bears your risk) - accounting only, Basel does not allow capital benefit
• BCVA = CVA - DVA
• FVA: Funding Valuation Adjustment - cost of funding collateral
• KVA: Capital Valuation Adjustment
• XVA = CVA + DVA + FVA + KVA + MVA

2. Why Basel Created CVA Capital Charge?

During 2007-2009 crisis, 2/3rd of counterparty credit losses were NOT from actual defaults, but from mark-to-market CVA losses as CDS spreads widened. Basel II only captured default, not spread widening.

Basel III introduced CVA charge as an additional capital charge requirement

Two approaches:

1. Basic CVA (BA-CVA): Standardized formula using EE, PD from CDS
2. SA-CVA: Sensitivity based, requires bank to have CVA desk that hedges

3. How to Calculate - Practical Steps

Step 1: Simulate Exposure
Monte Carlo of underlying (rates, FX) to get Expected Positive Exposure (EPE) profile over life of portfolio.

Step 2: Get PD from Market
PD implied from CDS spread: $PD \approx Spread / LGD$

Step 3: Wrong-Way Risk (WWR)

• Right-Way Risk: Exposure falls when PD rises (good)
• Wrong-Way Risk: Exposure rises when PD rises (deadly) - e.g., you sold USD/INR protection to an Indian importer, when INR collapses, his PD rises and your exposure rises simultaneously.
  Basel requires multiplier for WWR.

4. Case Laws and Disputes - Where CVA Became a Court Matter

Case Law 1: Lehman Brothers International (Europe) - The Mother of All CVA Disputes

When Lehman collapsed in 2008, 9,000+ ISDA masters were terminated. Core fight: What is close-out amount? Should it include CVA/DVA?

• Lomas v JFB Firth Rixson UKSC 32: UK Supreme Court ruled that Section 2(a)(iii) ISDA (suspension of payment on counterparty default) is valid. Non-defaulting party can suspend, but when calculating close-out, must include replacement cost. Replacement cost inherently includes CVA.[2012]
• Result: Administrators argued CVA should be zero because Lehman was already in default. Courts said: CVA must be calculated at time just before default, using market spreads. This created $2-5bn difference in claims.

Lesson: Your ISDA Close-out Amount clause must explicitly state whether CVA/DVA is included in Market Quotation.

Case Law 2: Deutsche Bank vs Unwired Planet & Credit Suisse - CVA as Unfair Pricing

European corporates sued banks 2013-2017 claiming banks overcharged CVA.

Allegation: Bank quoted swap rate including 80bps CVA but bank's internal CVA desk hedged it for 20bps, pocketing 60bps as hidden profit. Violation of MiFID duty of fair pricing.

• English High Court (2016): In Deutsche Bank vs Uniwired, court held CVA is part of fair value under IFRS 13, bank must disclose methodology if client asks, but no obligation to disclose internal hedging cost. CVA is subjective.

Lesson: Under MiFID II and RBI 2021 derivative guidelines, bank must give client Key Information: CVA methodology, but not breakdown.

Case Law 3: Indian Context - Rajshree Sugars vs Axis Bank (Madras HC 2008)

Already discussed in CRT, but CVA central:

Court noted: The collapse of Lehman Brothers and AIG due to extensive exposure to Credit Default Swaps threatening collapse of US financial system

Indian courts first recognized CVA concept: Loss on derivatives is not just MTM, but includes counterparty credit risk. Axis Bank had charged CVA on Rajshree's FX options.

Court upheld: If bank follows RBI circular DBOD No.BP.BC.86/21.04.157/2006-07 on derivatives, charging CVA is valid and not speculative.

Case Law 4: Company Voluntary Arrangement (CVA) Confusion - UK Debenhams Case

Note: In UK insolvency law, CVA also means Company Voluntary Arrangement - completely different from Credit Valuation Adjustment. But case law shows valuation disputes:

Landlord challenge to Debenhams CVA [2019] EWHC 2441: Landlords challenged CVA that reduced rents. Court held valuation advice received indicated all stores were over-rented. Whether CVA was unfairly prejudicial depends on vertical comparison (return in liquidation vs CVA) and horizontal comparison.

Why relevant? Same word, opposite use. When you search CVA case law, 90% results are insolvency CVAs . Always specify "Credit Valuation Adjustment" in legal agreements.

Case Law 5: Basel Regulatory Action - EU CVA Exemptions Litigation

EU adopted Basel III via CRR. Originally EU exempted corporate, pension fund, sovereign trades from CVA charge to avoid hurting real economy. Banks lobbied to keep exemption.

• 2020-2024: EU Commission decided to phase out exemption and adopt SA-CVA.
• European banks filed cases arguing double counting (CVA already in accounting). ECJ held CVA capital charge is distinct from accounting CVA - one is expected loss, other is unexpected loss due to spread volatility.

Case Law 6: Wrong-Way Risk - The Chinese Steel Trader Case (2015)

Chinese bank had commodity derivatives with steel traders. When steel prices collapsed, traders defaulted and exposure spiked (classic WWR). Bank had calculated CVA without WWR multiplier. Lost $400m.

Hong Kong SFC fined bank for inadequate CVA model, citing failure to capture Wrong Way Risk as required by Basel.

5. RBI / India Rules for CVA

1. Accounting: Ind AS 113 (Fair Value) requires CVA/DVA for all derivatives.
2. Capital: RBI Master Directions on Counterparty Credit Risk (based on SA-CCR) requires BA-CVA calculation for trades with financial counterparties.
3. Collateral: If you have daily margin (CSA), CVA reduces to ∼10 days Margin Period of Risk.
4. Disclosure: Pillar 3 disclosure must show CVA RWA separately.

6. Best Practice to Manage CVA

• CVA Desk: Central desk that charges business lines CVA and hedges with CDS
• Hedging: Buy CDS on major counterparties, sell CDS on yourself? Not allowed for capital.
• Mitigation: Netting agreement (ISDA), Collateral (CSA), Break clauses

Formula with collateral:
CVA = difference between value of risk-free derivatives and risky derivatives with same maturity