Function calibrate_base_correlation 

pub fn calibrate_base_correlation(
    discount: &Curve,
    survival: &Survival,
    recovery: Option<f64>,
    tranches: &[CdoTranche],
    tolerance: Tolerance,
) -> Result<CalibratedBaseCorrelation, CalibrationError>

Calibrates a base-correlation curve to a contiguous capital structure of CDO tranches on one index — the market-standard bootstrap.

The quotes are the tranches. Each carries its running coupon and its upfront, so at the solved correlation its value is zero; the residual is its npv, as for a par rung. The structure must attach at zero and be contiguous — each tranche attaching where the previous detaches, detachments strictly increasing — because a base correlation is defined on the cumulative tranche [0, D], and the mezzanine [A, D] is priced as the difference of two of them, the lower already solved.

Each detachment is solved by a bracketed bisection on [0, 1), passive throughout: correlation is never lifted (the model takes rho: f64), so no derivative is available and none is needed — the equity expected loss is monotone in its correlation, the bracket is fixed, and fifty halvings reach the step tolerance. The direction of monotonicity is read off the bracket’s ends, not assumed, so a seller’s tranche solves the same way.

recovery is the index’s market recovery; a tranche whose contract fixes its own uses that, and one that needs the market’s and finds None is refused by name before any solve. The discount and survival curves are the index’s, lifted passive.

Errors

CalibrationError::Malformed for an empty or non-contiguous structure or a missing recovery; CalibrationError::NoCorrelation for a tranche no correlation in [0, 1) reprices; CalibrationError::NoConvergence if a bracketed solve does not settle; a valuation error otherwise.