Modeling Counterparty Credit Exposure

Modeling Counterparty Credit Exposure

When To Use

• Calculating potential future exposure (PFE) profiles for OTC derivative portfolios
• Computing credit valuation adjustment (CVA) and debit valuation adjustment (DVA) for pricing or accounting (ASC 820 / IFRS 13)
• Assessing counterparty credit limits and concentration risk across netting sets
• Evaluating the impact of collateral agreements (CSAs) on exposure profiles
• Stress-testing counterparty exposure under adverse market scenarios
• Supporting regulatory capital calculations under SA-CCR or IMM [VERIFY: applicable regulatory framework]

Inputs To Gather

• Trade population: Full list of trades per counterparty, including notional, trade date, maturity, currency, and product type (IRS, CDS, FX forwards, equity options, etc.)
• Netting agreements: ISDA Master Agreement status, netting set definitions, and any close-out netting enforceability opinions [VERIFY: jurisdiction-specific enforceability]
• Collateral terms: CSA parameters — threshold, minimum transfer amount (MTA), independent amount, eligible collateral types, rehypothecation rights, margin period of risk (MPR)
• Market data: Yield curves, volatility surfaces, FX spot rates, credit spreads (CDS or bond-implied), correlation assumptions
• Counterparty credit data: Credit ratings, CDS spreads (or proxy spreads), probability of default (PD) term structures, loss given default (LGD) assumptions
• Own credit data: Entity CDS spreads or proxy for DVA calculation
• Simulation parameters: Number of Monte Carlo paths, time grid granularity, confidence level for PFE (typically 95th or 97.5th percentile), simulation horizon

Workflow

1. Map netting sets and collateral

   • Group trades by legal netting agreement; confirm enforceability per jurisdiction
   • Parse CSA terms: thresholds, MTAs, MPR, eligible collateral haircuts
   • Identify wrong-way risk exposures (counterparty credit quality correlated with exposure)

2. Calibrate market models

   • Select diffusion processes per risk factor (e.g., Hull-White for rates, GBM or local vol for equities/FX, reduced-form for credit)
   • Calibrate to current market data; document calibration targets and fit quality
   • Set correlation matrix across risk factors — use historical estimation with appropriate lookback window

3. Run Monte Carlo simulation

   • Simulate joint evolution of all risk factors across the time grid
   • Reprice each trade at each time step on each path (use analytic approximations or regression-based methods like Longstaff-Schwartz for early-exercise products)
   • Aggregate to netting-set level, apply close-out netting: net exposure = max(0, sum of MTMs within netting set)

4. Apply collateral dynamics

   • Model collateral calls with MPR lag (typically 10–20 business days for bilateral, 5 for cleared)
   • Apply thresholds, MTAs, and independent amounts per CSA
   • Compute collateralized exposure at each time step: E(t) = max(0, net MTM − collateral held)

5. Calculate exposure metrics

   • Expected Exposure (EE): Mean of positive exposures across paths at each time step
   • Potential Future Exposure (PFE): Quantile of exposure distribution (95th/97.5th percentile) at each time step
   • Expected Positive Exposure (EPE): Time-weighted average of EE over the profile
   • Peak PFE: Maximum PFE across the time grid
   • Effective EPE: Non-decreasing transformation of EPE for regulatory purposes

6. Compute CVA and DVA

   • CVA = integral of discounted EE × counterparty default probability × LGD over the exposure horizon
   • DVA = integral of discounted ENE (expected negative exposure) × own default probability × LGD
   • Use counterparty CDS spreads for market-implied PD; use rating-based PD for accounting if required [VERIFY: CVA methodology — market-implied vs. historical PD per firm policy]
   • Consider bilateral CVA (BCVA = CVA − DVA) and FVA if required

7. Stress test and validate

   • Run exposure profiles under stressed market scenarios (rate shocks, spread widening, FX moves)
   • Test sensitivity to correlation assumptions, number of simulation paths, and time-grid density
   • Compare model PFE against add-on based methods (SA-CCR) as a reasonableness check
   • Back-test exposure predictions against realized MTMs where historical data is available

Output

• Exposure profile report: Time-series charts of EE, PFE (with confidence level), and peak PFE per netting set and counterparty
• CVA/DVA summary: Unilateral CVA, DVA, and bilateral CVA per counterparty with breakdown by netting set
• Collateral impact analysis: Comparison of uncollateralized vs. collateralized exposure profiles showing CSA benefit
• Sensitivity tables: CVA sensitivity to credit spread moves (CS01), interest rate shifts, and correlation changes
• Wrong-way risk flags: Identification of netting sets where exposure and counterparty default are positively correlated
• Methodology documentation: Model choices, calibration details, simulation parameters, and all assumptions

Quality Checks

• Verify that netting-set groupings match legal documentation — incorrect netting inflates or deflates exposure
• Confirm collateral parameters (thresholds, MTA, MPR) are sourced from actual CSA terms, not defaults
• Check that the number of Monte Carlo paths produces stable results (re-run with doubled paths; PFE should not shift materially)
• Validate that EE converges to zero as trades approach maturity
• Ensure PFE at the 95th percentile exceeds EE at every time step — if not, check for simulation errors
• Cross-check CVA magnitude against market benchmarks: CVA as basis points of notional should be plausible given counterparty spread level
• Confirm discount curves and credit curves are as-of the same valuation date
• Flag any trades with missing market data or valuation failures — do not silently drop them from the simulation
• Mark all jurisdiction-dependent assumptions (netting enforceability, MPR regulatory minimums, capital framework) with [VERIFY]