Principle:Avhz RustQuant Yield Curve Construction

Knowledge Sources	Nelson & Siegel 1987 - Parsimonious Modeling of Yield Curves Svensson 1994 - Estimating and Interpreting Forward Interest Rates Hull - Options, Futures, and Other Derivatives
Domains	Fixed_Income, Yield_Curves, Market_Data
Last Updated	2026-02-07 20:00 GMT

Overview

A method for building a complete term structure of interest rates from observed market data points using interpolation and parametric curve fitting.

Description

Yield curve construction is the process of creating a continuous function of interest rates across all maturities from a discrete set of observed market rates. This is fundamental to fixed-income pricing, derivative valuation, and risk management.

The construction process involves:

1. Data collection: Gather observed rates at specific maturities (e.g., 1M, 3M, 6M, 1Y, 2Y, 5Y, 10Y, 30Y)
2. Curve type selection: Choose the representation (spot, forward, or discount)
3. Interpolation: Fill in rates between observed points
4. Fitting: Optionally fit a parametric model (e.g., Nelson-Siegel-Svensson)

Curve types:

• Spot curve: Zero-coupon rates for each maturity
• Forward curve: Instantaneous forward rates
• Discount curve: Discount factors for each maturity

Usage

Use yield curve construction when you need term structure rates for discounting cash flows, pricing bonds, or computing forward rates. This is the first step in most fixed-income and derivative pricing workflows.

Theoretical Basis

Nelson-Siegel-Svensson model:

$r(t)={\beta }_0+{\beta }_1\frac{1-e^{-t/{\tau }_1}}{t/{\tau }_1}+{\beta }_2(\frac{1-e^{-t/{\tau }_1}}{t/{\tau }_1}-e^{-t/{\tau }_1})+{\beta }_3(\frac{1-e^{-t/{\tau }_2}}{t/{\tau }_2}-e^{-t/{\tau }_2})$

Parameters:

• beta_0: Long-term rate level
• beta_1: Short-term component (slope)
• beta_2: Medium-term hump (curvature)
• beta_3: Second hump (Svensson extension)
• tau_1, tau_2: Decay parameters

Relationships between curve types:

• Discount factor: D(t) = exp(-r(t) * t)
• Forward rate: f(t) = -d/dt ln(D(t))

Related Pages

Implemented By

• Implementation:Avhz_RustQuant_Curve_new

Uses Heuristic

• Heuristic:Avhz_RustQuant_Interpolation_Method_Selection