Principle:Avhz RustQuant Curve Interpolation

Knowledge Sources	Burden & Faires - Numerical Analysis Nelson & Siegel 1987
Domains	Numerical_Methods, Interpolation, Fixed_Income
Last Updated	2026-02-07 20:00 GMT

Overview

Mathematical methods for estimating values between known data points on a yield curve, including linear interpolation, exponential interpolation, and parametric model fitting.

Description

Curve interpolation is the process of estimating interest rates at maturities not directly observed in market data. Different interpolation methods have different properties:

Linear interpolation: Simple, preserves data points, but produces discontinuous forward rates
Exponential interpolation: Ensures positive rates, smoother discount factors
Cubic spline: Smooth first and second derivatives, complex to implement
Nelson-Siegel-Svensson fitting: Parametric model capturing level, slope, and curvature

The choice of interpolation method affects derivative pricing, hedging, and risk calculations.

Usage

Use curve interpolation when you need rates at dates not present in the original market data. The method is applied automatically by the Curve struct when get_rate() is called for an out-of-sample date.

Theoretical Basis

Linear interpolation:

$r (t) = r_{1} + \frac{r_{2} - r_{1}}{t_{2} - t_{1}} (t - t_{1})$

Exponential interpolation:

$D (t) = D (t_{1}) {(\frac{D (t_{2})}{D (t_{1})})}^{\frac{t - t_{1}}{t_{2} - t_{1}}}$

where D(t) = exp(-r(t) * t) are discount factors.

Nelson-Siegel-Svensson (NSS) fitting: The curve is fit by minimizing a log-cosh loss function between observed rates and the NSS model rates using particle swarm optimization (via the argmin crate).

Related Pages

Implemented By

Implementation:Avhz_RustQuant_Curve_get_rate

Uses Heuristic

Heuristic:Avhz_RustQuant_Interpolation_Method_Selection

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