yield-curves

Yield curve interpolation and parametric fitting for fixed income, in pure Rust with zero dependencies.

Interpolation methods

• Linear — piecewise linear, transparent baseline.
• Cubic spline — natural cubic spline (C² continuous) via Thomas algorithm.
• PCHIP (new in 0.2) — Fritsch-Carlson monotone cubic Hermite. C¹ continuous; preserves monotonicity and never overshoots adjacent anchors. Use when natural cubic spline produces spurious humps with sparse data.
• Nelson-Siegel (1987) — 4-parameter parametric fit.
• Svensson (1994) — 6-parameter parametric fit; official model used by BCB (Brazil), ANBIMA, and the ECB's AAA-rated euro-area curve.

Compounding & forward rates (new in 0.2)

The compounding module turns interpolated rates into discount factors and forward rates under any of: continuous, periodic (Periodic(n) covers annual / semi / quarterly / monthly / Brazil-252), and simple compounding.

use yield_curves::{CubicSplineCurve, YieldCurveInterpolator};
use yield_curves::compounding::{discount_factor, forward_rate, Compounding};

let curve = CubicSplineCurve::fit(&[(1.0, 13.0), (2.0, 13.5), (5.0, 13.8)]).unwrap();
let rate_pct = curve.rate_at(3.0);

// Discount factor for 3 years under continuous compounding.
// Caller is responsible for converting percent → decimal.
let df = discount_factor(rate_pct / 100.0, 3.0, Compounding::Continuous);

// Implied forward rate between t1 = 1y and t2 = 5y.
let fwd = forward_rate(
    curve.rate_at(1.0) / 100.0, 1.0,
    curve.rate_at(5.0) / 100.0, 5.0,
    Compounding::Continuous,
).unwrap();

Functions live outside the YieldCurveInterpolator trait on purpose: rate unit (% vs decimal) and compounding convention are caller concerns, not properties of the curve shape.

No dependency on ndarray, argmin, or any numerical crate. The Nelder-Mead simplex optimizer used by the parametric fits is implemented internally.

Quick start

use yield_curves::{CubicSplineCurve, NelsonSiegelCurve, YieldCurveInterpolator};

// Brazilian nominal yield curve from LTNs / NTN-Fs.
// x is time in years, y is the observed yield in percent.
let points = [
    (1.0, 13.98),
    (2.5, 13.51),
    (4.0, 13.45),
    (7.0, 13.57),
    (10.0, 13.80),
];

let cubic = CubicSplineCurve::fit(&points).unwrap();
let rate_5y = cubic.rate_at(5.0);

let ns = NelsonSiegelCurve::fit(&points).unwrap();
let (beta0, beta1, beta2, tau) = ns.parameters();

Conventions

The x-axis is time in years. Convert from calendar / business days at the call site:

Extrapolation is flat outside the observed range — the rate of the nearest observed anchor is returned. Parametric models in particular diverge quickly outside the fitted range, so flat extrapolation is the safer default for financial use.

When to pick what

• Linear — transparent, monotonic, used as a baseline or when anchors are already smoothed. Not C¹.
• Cubic spline — smoothest interpolation that still passes through every anchor exactly. Good default when you trust your anchor points.
• PCHIP — pick this over cubic spline when sparse anchors produce visible overshoots/oscillations, or when monotonicity must be preserved (e.g. an inflation index). C¹ continuous (less smooth than spline) but shape-preserving.
• Nelson-Siegel — parsimonious 4-parameter fit. Produces monotonic or single-hump curves only. Use when you want a smooth parametric form for research or when your anchors are noisy.
• Svensson — adds a second hump to NS. Standard for sovereign curves (BCB/ANBIMA/ECB publish Svensson). Needs at least 6 anchor points and benefits from regularly spaced maturities.

Both parametric methods perform a sanity check on the fitted parameters and return [YieldCurveError::FitFailed] if the optimizer lands on an implausible mode (typical symptom with few anchors or anchors that don't match the parametric shape). In that case, fall back to the cubic spline.

License

Licensed under either of MIT or Apache License, Version 2.0 at your option.