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XVA Sensitivities

XvaEngine::run computes sensitivities of every XVA value with the same tape-based AD used for pricing: the market model is built from DualFwd leaves, paths are simulated as DualFwd, aggregators are differentiated, and one reverse sweep returns the gradient with respect to every registered leaf. No bumping and re-simulation is required.

Labels

result.sensitivities: Option<Vec<(String, f64)>> pairs a label with \(\partial\text{XVA}/\partial\text{leaf}\):

LabelLeaf
curve quote identifiers (OIS_USD_SOFR_5Y, OIS_CLP_ICP_2Y, FloatFloatCrossCurrencySwap_USD_SOFR_ICP_CLP_5Y)curve pillars mapped back to quotes through the IFT
volatility pillar labels from HullWhiteTimeDependentVolatility::with_pillar_labels() (calibration quote identifiers such as CapletFloorlet_USD_SOFR_3M_1Y_Absolute_0.045_Straddle_Black)calibrated LGM sigma pillars
FX.<pair>.spot, FX.<pair>.vol (e.g. FX.CLPUSD.spot)FX spot and lognormal FX volatility per FxModelConfig
<credit_index>.pillar_<i>survival pillars of a bootstrapped credit curve
funding_spread.<date> or <funding_index>.<date>funding spread term structure

Values are aggregated across all netting sets in the run. To obtain per-set sensitivities run the engine once per netting set.

Example

let result = engine.run(&mut netting_sets)?;
let mut sens = result.sensitivities.unwrap_or_default();
sens.sort_by(|a, b| b.1.abs().partial_cmp(&a.1.abs()).unwrap_or(std::cmp::Ordering::Equal));
for (label, value) in sens.iter().take(10) {
    println!("{label:<55} {value:>12.4}");
}

Typical top rows for the examples/cva portfolio are the long-dated SOFR OIS quotes (through both the exposure and the system discounting), the cross-currency basis quotes and FX.CLPUSD.vol.

Notes

  • The deterministic system-curve discounting step (\(P(0,t_k)\) from the domestic curve) is not differentiated, so curve sensitivities exclude that term.
  • Path noise is common to value and gradient: since sensitivities come from the same paths, they are consistent with the reported XVA (no bump-noise), but they still carry Monte Carlo error that decreases with n_paths.
  • Sensitivities to lambda, rho and constant sigma/fx_vol configuration values are available where those values are leaves (FX.<pair>.vol); lambda and rho are treated as constants.
  • Validate by rerunning with a Scenario on the base quotes (see Scenarios) and the same seed.