Modeling Xva Adjustments

Modeling XVA Adjustments

When To Use

• Computing credit valuation adjustment (CVA) or debit valuation adjustment (DVA) for OTC derivative portfolios
• Quantifying funding valuation adjustment (FVA) to reflect treasury funding costs/benefits on uncollateralized or partially collateralized positions
• Estimating capital valuation adjustment (KVA) to allocate regulatory capital costs (SA-CCR, IMM, FRTB) back to individual trades
• Calculating margin valuation adjustment (MVA) for initial margin costs under UMR or CCP requirements
• Performing portfolio-level XVA aggregation with netting set and CSA-aware exposure profiles
• Designing XVA hedging strategies or evaluating incremental XVA on new trades

Inputs To Gather

• Trade population: Trade-level details (notional, maturity, currency, product type) for each netting set
• CSA / margin terms: Threshold, minimum transfer amount, independent amount, eligible collateral, rehypothecation rights, variation margin frequency, initial margin model (ISDA SIMM vs. schedule) [VERIFY against actual CSA documents]
• Counterparty credit data: CDS spreads or mapped credit curves, recovery rate assumptions, rating/sector if using proxy curves
• Own-credit data: Entity CDS spread or internal funding curve for DVA and FVA
• Market data: Yield curves, FX rates, volatility surfaces, correlation assumptions for exposure simulation
• Funding curve: Internal cost-of-funds curve distinguishing secured vs. unsecured rates; FVA spread = unsecured funding rate − OIS
• Regulatory parameters: SA-CCR alpha factor, supervisory risk weights, cost-of-capital rate (typically 8–12%), capital horizon [VERIFY against current Basel III/IV regime applicable to entity]
• Simulation parameters: Number of Monte Carlo paths, time grid granularity, diffusion model choice (GBM, local vol, stochastic vol)

Workflow

1. Scope & segmentation — Identify netting sets, confirm CSA terms per netting set, classify trades as collateralized/uncollateralized/partially collateralized. Determine which XVA components are in scope (CVA, DVA, FVA, KVA, MVA).

2. Exposure simulation — Run Monte Carlo simulation to generate future portfolio values on a time grid. Compute expected positive exposure (EPE) and expected negative exposure (ENE) profiles per netting set, applying CSA margining logic (threshold, MTA, margin period of risk).

3. CVA calculation — Integrate discounted EPE against counterparty default probability:

   • CVA ≈ Σ_t [ DF(t) × EPE(t) × (1 − R_cpty) × ΔPD_cpty(t) ]
   • Use counterparty CDS-implied hazard rates or mapped proxy curves
   • Apply wrong-way risk adjustments where exposure is correlated with counterparty credit quality

4. DVA calculation — Mirror CVA using ENE and own default probability:

   • DVA ≈ Σ_t [ DF(t) × ENE(t) × (1 − R_own) × ΔPD_own(t) ]
   • Note DVA accounting treatment varies: IFRS 13 requires DVA in P&L; some desks exclude from pricing [VERIFY entity's DVA policy]

5. FVA calculation — Compute funding cost/benefit on expected unsecured exposure:

   • FVA ≈ Σ_t [ EPE(t) × s_fund(t) × Δt ] − Σ_t [ ENE(t) × s_fund(t) × Δt ]
   • Where s_fund is the entity's funding spread over OIS
   • Distinguish FCA (funding cost) from FBA (funding benefit) if reported separately

6. KVA calculation — Estimate lifetime cost of regulatory capital:

   • Compute future capital profiles using SA-CCR EAD at each simulation date
   • KVA ≈ Σ_t [ DF(t) × h_capital × RegulatoryCapital(t) × Δt ]
   • h_capital = hurdle rate (cost of equity minus risk-free rate, typically 6–10%)
   • [VERIFY applicable capital framework: SA-CCR vs. IMM; Basel III vs. IV timeline]

7. MVA calculation — Quantify cost of funding initial margin over trade life:

   • Project future IM using ISDA SIMM or CCP schedule on simulated portfolios
   • MVA ≈ Σ_t [ DF(t) × E[IM(t)] × s_fund(t) × Δt ]
   • For bilateral trades under UMR, confirm phase-in applicability [VERIFY UMR phase and AANA threshold]

8. Aggregation & allocation — Sum components to total XVA per netting set and portfolio-wide. Allocate incremental XVA to individual trades using Euler allocation or stand-alone/incremental decomposition for pricing and desk-level P&L attribution.

9. Hedging strategy — Identify primary XVA risk drivers:

   • CVA hedge: Single-name CDS or index CDS (iTraxx/CDX) for spread risk; interest rate swaps for exposure profile
   • FVA hedge: Secured funding or collateral transformation trades
   • Assess hedge effectiveness, basis risk, and cost-of-hedge vs. XVA reduction

10. Sensitivity & stress testing — Run bumps on key inputs (credit spreads ±10bp, funding spreads ±5bp, rates ±25bp, correlation shifts) and report XVA Greeks (CS01, IR01, FVA01). Stress-test under adverse scenarios (counterparty downgrade, funding stress, margin call spikes).

Output

• XVA summary table: CVA, DVA, FVA (FCA/FBA split), KVA, MVA per netting set and total portfolio, with base-case values and percentage of notional
• Exposure profiles: EPE and ENE time series charts per netting set, with and without collateral
• Capital profile: Projected regulatory capital over time under SA-CCR / IMM
• IM projection: Expected initial margin trajectory for MVA computation
• Sensitivity report: XVA Greeks (CS01, IR01, FVA01, CorrelSens) in tabular format
• Stress results: XVA under 3–5 stress scenarios with narrative on key drivers
• Hedging recommendation: Instruments, notional sizing, expected hedge ratio, residual risk, and estimated hedge cost
• Methodology documentation: Simulation assumptions, model choices, recovery rates, proxy mapping logic, and any overrides

Quality Checks

• Confirm EPE/ENE profiles converge with sufficient Monte Carlo paths (check standard error < 1% of mean)
• Validate CVA against analytic approximation (e.g., semi-analytic formula for vanilla swaps) as a sanity check
• Ensure FVA sign convention is consistent: positive FVA = cost to the entity for net lending positions
• Verify netting set boundaries match legal documentation (ISDA Master Agreement scope)
• Cross-check CDS-implied default probabilities against rating-implied benchmarks for reasonableness
• Confirm KVA capital calculation matches independently computed SA-CCR EAD for spot date
• Validate that collateral modeling correctly reflects CSA terms (threshold, MTA, rounding, eligible currencies)
• Review incremental XVA for a new trade: should be bounded between stand-alone XVA (upper) and marginal XVA (lower)
• Flag any counterparty without liquid CDS data — proxy mapping methodology must be documented and reviewed