How do banks backtest CVA models?

Question

AcadiFi · Accepted Answer

CVA backtesting is challenging because CVA is risk-neutral and forward-looking — you can't observe the 'correct' CVA. Banks break backtesting into three components that CAN be tested.

**1. Exposure model backtesting** — compare simulated exposure distributions to realized MtM paths. Select a representative counterparty, say Aldridge Chemicals (rated A, mix of IRS and FX forwards). Every trading day for 250 days:
- Generate Monte Carlo forecast: EE at 1W, 1M, 3M, 1Y horizons
- After 1W/1M/3M/1Y, observe actual MtM
- Test whether actual MtM falls within the forecasted distribution at expected frequency

Kupiec's POF test or Christoffersen's conditional coverage test apply here, treating the exceedance as a binary outcome.

**2. PD / credit spread backtesting** — compare model-implied PDs from CDS curves to observed defaults over time. Group counterparties by rating bucket, count actual defaults, compare to expected.

**3. CVA sensitivities backtesting** — daily CVA P&L should approximately equal (Σ sensitivities × market moves) + time decay. Large unexplained P&L indicates model error.

**Overall governance**:

| Test | Frequency | Tolerance |
|---|---|---|
| EE backtest | Quarterly | <5% exceedances at 95% |
| PD backtest | Annually | Rating PDs within 1 grade |
| CVA P&L attribution | Daily | <10% unexplained |
| Benchmarking vs peers | Annually | Within reasonable range |

Regulators (SR 11-7 in the US, SS 3/18 in the UK) require formal CVA model validation covering data quality, conceptual soundness, and ongoing performance. The FRM curriculum emphasizes that CVA backtesting is a combination of exposure backtesting (market-risk style), PD calibration review, and daily P&L attribution — no single test validates CVA as a whole.

For FRM, remember: you backtest the INPUTS to CVA (exposure, PDs), not CVA itself.

How do banks backtest CVA models?

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