Advanced Yield Curve Modeling in Python: Implementing Nelson-Siegel and Svensson Models

Welcome! When I first started diving deep into fixed income analytics, one of the most powerful tools I encountered was the yield curve. But simply looking at market rates wasn’t enough; I needed robust models to understand its shape and dynamics. That’s where models like Nelson-Siegel (NS) and its extension, Nelson-Siegel-Svensson (NSS), come into play. They provide a structured way to represent the entire term structure of interest rates with just a few interpretable parameters.

This tutorial is designed as an advanced, hands-on guide. We’ll go beyond the theory and build these models from scratch in Python. Using real market data, specifically US Treasury yields, we’ll implement the NS and NSS formulas, calibrate their parameters using optimization techniques, compare their effectiveness and analyze how these parameters change over time. Our toolkit will primarily involve core scientific Python libraries: NumPy for numerical operations, SciPy for optimization, Pandas for data handling and Matplotlib for visualization. Prepare to translate mathematical concepts into practical code and gain a deeper understanding of yield curve behavior.

Table of Contents

• Yield Curve Fundamentals & Model Overview: Review yield curve basics and introduce the…