Bond Spread Calculations

Implements five spread methodologies for fixed income analytics with Bloomberg YAS parity and data-source neutral architecture.

Spread Hierarchy (Simplest → Most Complex)

Spread	What It Measures	Complexity	Curve Required
G-Spread	Yield over interpolated government bond	Low	Gov't par curve
I-Spread	Yield over interpolated swap rate	Low	Swap par curve
Z-Spread	Constant spread over zero curve matching dirty price	Medium	Zero/spot curve
ASW	Spread in swap market terms	Medium	Zero + forward curves
OAS	Spread after removing embedded option value	High	Zero + vol surface

Typical ordering: OAS ≤ Z-Spread ≈ ASW < I-Spread < G-Spread for investment-grade bonds.

Quick Reference

Z-Spread (Primary Spread)

Solve for constant Z where:

code

P_dirty = Σ [CF_i / (1 + (s_i + Z)/2)^(2×t_i)]  // Semi-annual
P_dirty = Σ [CF_i × exp(-(s_i + Z) × t_i)]       // Continuous

Solver: Brent's method (recommended) or Newton-Raphson

•Tolerance: 1e-8 (~0.001 bp)
•Bounds: [-0.10, 1.00]
•Initial guess: YTM - benchmark_YTM

I-Spread / G-Spread

code

I-Spread = Bond_YTM - Interpolated_Swap_Rate(maturity)
G-Spread = Bond_YTM - Interpolated_Govt_Yield(maturity)

ISDA interpolation: Linear on calendar days between bracketing tenors.

ASW (Par-Par Convention - Bloomberg Default)

code

ASW = (PV_bond_coupons_at_swap_rates - P_dirty) / PV01_annuity

OAS

Requires Hull-White model with trinomial tree or Monte Carlo. See references/spreads.md.

Currency Conventions (Post-LIBOR)

Currency	RFR	Day Count	Spot	Fixed Freq
USD	SOFR	ACT/360	T+2	Annual
EUR	€STR	ACT/360	T+2	Annual
GBP	SONIA	ACT/365F	T+0	Annual

Government benchmarks: USD=Treasuries, EUR=Bunds, GBP=Gilts

Implementation Checklist

•Curve infrastructure - Zero rates, discount factors, forward rates, par rates with interpolation
•Day count functions - ACT/360, ACT/365F, ACT/ACT ICMA, 30/360
•Root-finding solver - Brent's method with fallback to bisection
•Cash flow generation - Handle settlement, ex-dividend, accrued interest

Detailed References

•Spread calculations: See references/spreads.md for formulas, solver algorithms, edge cases
•Curve construction: See references/curves.md for bootstrapping, interpolation methods
•Market conventions: See references/conventions.md for currency-specific details

Rust Data Structures

rust

pub trait YieldCurve {
    fn zero_rate(&self, t: f64) -> f64;
    fn discount_factor(&self, t: f64) -> f64;
    fn forward_rate(&self, t1: f64, t2: f64) -> f64;
    fn par_rate(&self, tenor: f64) -> f64;
}

pub struct BondSpreadResult {
    pub z_spread: Option<f64>,
    pub i_spread: Option<f64>,
    pub g_spread: Option<f64>,
    pub asw_par: Option<f64>,
    pub asw_market: Option<f64>,
    pub oas: Option<f64>,
}

pub enum DayCount { Act360, Act365Fixed, ActActICMA, ActActISDA, Thirty360, ThirtyE360 }
pub enum Compounding { Simple, Annual, SemiAnnual, Quarterly, Continuous }
pub enum InterpolationMethod { Linear, LogLinear, CubicSpline, MonotoneConvex }

Validation Targets

•Roundtrip: Input swap rates must reprice exactly (< 1e-10)
•Bloomberg parity: Z-spread within ±0.05 bp, OAS within ±0.5 bp
•Arbitrage-free: Positive forwards, monotonic discount factors