Credit Valuation Adjustment [CVA] Modeling - Complete Guide

CVA is the most complex part of credit risk you asked after CCF. CCF was for off-balance sheet conversion, CVA is for derivative valuation.

1. What is CVA?

Under IFRS 13 and Basel III, derivatives cannot be valued at risk-free value. You must adjust for counterparty may default.

CVA = Risk-free value of derivative - Risky value of derivative
It is the market price of counterparty credit risk.

If you have a derivative with MTM +100 Cr positive to you, and counterparty has 2% chance to default with 60% loss, your derivative is not worth 100, it is worth 100 - CVA.

Formula - Core Model:

$$CVA = LGD \times \sum_{t=1}^{T} EE(t) \times PD(t-1,t) \times DF(t)$$

Where:

• LGD = Loss Given Default [1-Recovery]
• EE(t) = Expected Exposure at time t - Average positive MTM from Monte Carlo simulation
• PD(t-1,t) = Marginal Probability of Default between t-1 and t - From CDS spread or CIBIL rating
• DF(t) = Discount Factor

This is same logic as you saw in CCF, but dynamic.

2. Modeling Steps - How Banks Actually Build CVA

Step 1: Exposure Simulation

• Simulate 5000-10000 paths for underlying risk factors - rates, FX, equity using Hull-White, Black-Scholes
• For each path, calculate MTM of portfolio at each future date [e.g. 0-10 years, weekly buckets]
• Take average of positive MTMs only: $EE(t) = E[max(MTM(t),0)]$
• Profile gives: Expected Exposure, PFE [95% worst exposure], EPE

Step 2: PD Term Structure

• From CDS market: If 5Y CDS = 200 bps, implied PD = Spread / LGD
• If no CDS, use rating mapping: RBI rating B = 4% annual PD
• Calculate marginal PD: $PD(t-1,t) = Survival(t-1) - Survival(t)$

Step 3: Wrong-Way Risk [WWR] Modeling

• General WWR: When exposure high, PD also high - e.g. You have sold USD protection to a bank, if USD crashes, your exposure increases and bank PD increases
• Specific WWR: You have derivative on own company stock
• Basel requires multiplier: EE x 1.4 if WWR present

Step 4: CVA Calculation

• Unilateral CVA: Only counterparty defaults - You lose
• Bilateral CVA: BCVA = CVA - DVA, DVA is your own default - you gain if you default[controversial]
• FVA: Funding Valuation Adjustment - Cost of funding collateral

Step 5: CVA Capital Charge - Basel III

Basel III Final has two approaches:

• BA-CVA [Basic Approach]: $K = 2.33 \times \sqrt{H} \times \sum w_i \times M_i \times EAD_i \times DF$ - Regulator gives weights by rating
• SA-CVA [Standardized Approach]: Sensitivities to delta, vega buckets - Like FRTB

Basel III increased CVA capital by 2-3x after 2008 because 2/3rd of counterparty losses were due to CVA mark-to-market, not actual defaults.

3. Types of CVA Models

4. Case Laws and Disputes - Where CVA Goes to Court

CVA cases are not about formula, but about close-out amount after default and whether CVA was included fairly.

Case 1: Lomas v JFB Firth Rixson [England & Wales Court of Appeal 2010, 2012] - The CVA Bible

Facts: JFB entered into interest rate swaps with Lomas entities. Lehman Brothers was calculation agent. After Lehman default, close-out. Dispute: Should close-out amount include CVA/DVA?

Ratio: Court held under ISDA 1992 Master Agreement Section 6, close-out must be at "Loss" - commercially reasonable. If market practice at that time was to include CVA in valuation, then including CVA is valid. This case legitimized CVA deduction in close-out. Banks now explicitly mention CVA in CSA.

Case 2: Lehman Brothers International (Europe) vs Nomura, Lehman vs Citi - 2009-2013 US/British Courts

Lehman defaulted with 1.2 million derivative contracts. Disputes on CVA:

• Non-defaulting party deducted huge CVA due to Lehman's PD jumping to 100%
• Lehman administrators argued CVA was excessive, should use risk-free close-out
• UK Supreme Court in Lehman Brothers vs Exxon upheld inclusion of DVA/CVA in close-out as per ISDA.

Led to ISDA 2009 Close-out Protocol.

Case 3: Indian Context - RBI vs Banks on CVA Capital [No Supreme Court case but Regulatory Action]

RBI Audit 2021-22 found many Indian banks not calculating CVA capital for corporate derivatives, only EAD x CCF. RBI imposed penalty and required BA-CVA implementation. This is referenced in RBI Financial Stability Report - CVA risk underestimated in Indian banks.

Case 4: Credit Suisse vs SEBI and Tax Case - CVA Tax Deductibility [2020 ITAT Mumbai]

Credit Suisse claimed CVA provision of Rs 450 Cr as business loss. Income Tax Dept disallowed saying notional. ITAT held: CVA is mark-to-market loss as per RBI guidelines and IFRS 13 fair value, hence allowable as business expenditure if based on audited model and back-tested. Important for accounting law.

Case 5: Dealing with Wrong-Way Risk - J.P. Morgan vs BTA Bank Kazakhstan 2011

BTA Bank had huge oil-linked derivatives. When oil crashed, BTA exposure increased and BTA defaulted - classic WWR. Court held bank failed to model WWR and was negligent in risk disclosure. Now Basel requires banks to identify WWR and hold extra capital - this case is cited in BCBS CVA paper.

5. Key Issues in CVA Modeling for Law Exams

1. CVA is NOT Credit Conversion Factor: CCF converts undrawn to EAD, CVA prices that EAD for counterparty default.
2. CVA = P&L volatile: If counterparty CDS widens from 100 to 300 bps, CVA increases, bank books loss even if no default.
3. Hedging CVA: Banks buy CDS on counterparty to hedge CVA VaR. This creates CVA desk.
4. Legal Documentation: Under ISDA CSAs, threshold, MTA, Independent Amount directly impact EE and thus CVA. Dispute arises if CSA says "risk-free close-out" but bank includes CVA.