regit-curves

Audit-grade interest-rate yield curve bootstrap and interpolation. Zero-dependency, pure Rust.

What it does

regit-curves bootstraps interest-rate yield curves from market instruments — deposits, FRAs, STIR futures, fixed-floating vanilla swaps, OIS swaps, and basis swaps — and exposes the resulting curve as four mutually consistent views: discount factor, zero rate, instantaneous forward and par yield.

It supports both the classical single-curve convention and the post-2008 multi-curve (OIS-discounted, IBOR-projection) framework, and ships a documented family of interpolation methods — from log-linear on discount factors (Hagan & West's recommended default) through Steffen and Hyman monotone splines, Fritsch-Carlson monotone cubics, and natural / clamped / not-a-knot cubic splines.

Every formula is hand-rolled from primary paper sources with no external dependencies. A regulator, quant auditor, or new engineer can open any source file and trace every number to a citable derivation in MATH.md.

Why this crate exists

An interest-rate curve is the input to every discount, every forward, and every fixed-income risk number. Markets quote a sparse, discrete set of instruments — but pricing and risk need a continuous curve.

The naive fix is to interpolate the quotes. Interpolation silently changes prices. Splining zero rates introduces non-monotone forwards; piecewise linear discount factors give negative forwards; the wrong interpolation domain (zero rate vs log-discount vs instantaneous forward) re-prices the same instrument differently. A curve with either defect produces mispriced swaps, unstable hedges, and risk numbers that cannot be trusted, and the defect is invisible unless you test for it.

regit-curves solves this at the bootstrap level — by re-pricing every bootstrap instrument to zero residual at every curve node — and at the interpolation level — by exposing the interpolation method as a first-class choice, propagating it consistently through every derived view, and citing its mathematical and convergence properties to the primary source.

This sits within Regit OS: regit-curves is the yield-curve layer. It is self-contained — day-count conventions, calendar arithmetic, and every numerical primitive ship inside the crate — and produces a clean, audit-traceable curve for pricing and risk downstream.

Quick start

[dependencies]
regit-curves = "1.0"

See examples/quickstart.rs for a complete working example covering single-curve bootstrap, multi-curve OIS-discounting, and the full set of derived views.

Curve views

Conversions between any two views are total and round-trip exactly at the curve nodes.

Bootstrap instruments

Interpolation methods

Each method is C^{k (or piecewise C}k) in the documented sense and is propagated consistently through every derived view.

Note on ConvexMonotone. Hagan–West Method 7 is designed for positive monotone non-increasing discount factors — the canonical yield-curve setting in which the paper proves the non-negative-forward guarantee. On that domain it agrees bit-exactly with independent implementations (verified against tf-quant-finance to 2.2 × 10⁻¹⁶ relative). Outside that domain — oscillating inputs where the implied discrete forwards change sign — the §3.6 proof no longer applies and the fhat clipping per §4 eq. 25 (used here verbatim) can differ from implementations that omit it. Use CubicSpline or HermiteBessel for general-purpose non-monotone interpolation.

Architecture

src/
  lib.rs                       # Module declarations + re-exports
  types.rs                     # Date, Tenor, Compounding, Daycount enum
  errors.rs                    # Typed errors — bootstrap and curve
  math/                        # Hand-rolled numerical primitives
    linear_solve.rs            # Gaussian elimination + Cholesky
    tridiag.rs                 # Thomas algorithm for spline systems
    brent.rs                   # Bracketed root-finder (Brent 1973)

  instruments/                 # Bootstrap instruments
    basis_swap.rs              # Tenor / cross-currency basis swap
    bond.rs                    # Coupon-bearing bond
    deposit.rs                 # Money-market deposit
    fra.rs                     # Forward-rate agreement
    future.rs                  # STIR future with convexity adjustment
    ois_swap.rs                # OIS swap
    schedule.rs                # SwapSchedule helper (regular schedules)
    swap_fixed_float.rs        # Vanilla fixed-floating swap

  interpolation/               # Interpolation methods
    convex_monotone.rs         # Hagan–West Method 7 (monotone-convex)
    cubic_spline.rs            # natural / clamped / not-a-knot
    hermite_bessel.rs          # Bessel-slope Hermite
    linear.rs                  # piecewise linear
    linear_in_zero.rs          # Hagan & West default
    log_linear.rs              # piecewise log-linear
    monotone_cubic.rs          # Fritsch & Carlson 1980
    monotone_hyman.rs          # Hyman 1983 filter
    monotone_steffen.rs        # Steffen 1990
    piecewise_constant_forward.rs

  curves/                      # Curve views and conversions
    discount.rs                # DiscountCurve — canonical
    zero.rs                    # ZeroCurve     — z(t)
    forward.rs                 # ForwardCurve  — f(t)
    par.rs                     # ParCurve      — par yields

  bootstrap.rs                 # Sequential iterative bootstrap engine
  multi_curve.rs               # OIS-discounted multi-curve bootstrap

One file, one domain. Each function is pure, deterministic, and composable.

Testing

cargo test                      # 792 tests
cargo run --example quickstart  # End-to-end single-curve + multi-curve workflow
cargo bench                     # Criterion benchmarks

629 unit tests — golden values from primary papers, every error path, every accessor, day-count round-trips against ISDA 2006 §4.16 worked examples, daycount and calendar arithmetic on [1900..2100], Hyman 1983 RPN15A monotonicity oracle, Steffen oracle fixture, Brent root-finder golden roots, Thomas tridiagonal solver cross-check against dense Gaussian, and instrument residual-on-flat-curve identities.

29 integration tests across six suites: golden anchors transcribed from QuantLib's PiecewiseYieldCurve test suite (Modified BSD) and Google tf-quant-finance's bond_curve_test.py (Apache-2.0); curve-view round-trip identities (discount ↔ zero ↔ forward ↔ par); arbitrage oracle (positive discount factors, monotone discount); the Hyman 1983 RPN15A monotonicity discriminator; proptest invariants (bootstrap_never_panics under random inputs); and a full multi-curve end-to-end OIS + 3M IBOR re-pricing certificate.

134 doc-tests — every public item carries a runnable example.

Code quality

• #![forbid(unsafe_code)] crate-wide
• clippy::pedantic with zero warnings
• Every public function documented with its mathematical reference
• No unwrap() or panic!() in library code — all failure paths typed
• Deterministic: same input produces bit-identical output
• WASM-clean: cargo build --target wasm32-unknown-unknown with no changes
• 792 tests — unit, integration, proptest invariants, doc-tests — plus criterion benchmarks (see Testing)

The crate is std-only — curve nodes are variable-size, so clean Vec-based code beats no_std gymnastics for the heavy linear algebra. Zero runtime dependencies are still enforced.

Dependencies

Runtime: zero. Only std. No nalgebra, no argmin, no libm, no FFI. Every linear solver, every root-finder, every interpolation algorithm is hand-rolled from its primary source.

License and supply-chain policy is enforced via cargo-deny (deny.toml). No copyleft dependencies.

Algorithms

All implemented from primary paper sources. No ports from Python, no reading existing Rust crates.

Cross-checked against published numerical examples from Hagan & West (2008 worked tables), QuantLib's PiecewiseYieldCurve test suite, and Andersen & Piterbarg, Interest Rate Modeling (Atlantic Financial Press, 2010), vol. 1 §6.

Documentation

• MATH.md — Full mathematical derivations for every algorithm
• CHANGELOG.md — Release history
• SECURITY.md — Vulnerability disclosure policy

License

Apache License 2.0. See LICENSE and NOTICE.

Copyright 2026 Regit.io — Nicolas Koenig

Part of Regit OS — the operating system for investment products. From Luxembourg.