Implement the Nelson-Siegel-Svensson Yield Curve in Python

Ever looked at bond market data and wondered how to make sense of all those different interest rates across different time horizons? That relationship between the yield on a bond and its time to maturity is captured by the yield curve, a fundamental concept in finance. It tells us about market expectations for future interest rates, economic growth and inflation. Accurately modeling this curve is crucial for everything from pricing bonds and derivatives to managing risk and informing monetary policy decisions.

One of the most popular and practical methods for this is the Nelson-Siegel-Svensson (NSS) model. When I first started working with fixed income data, I found the NSS model incredibly useful because it balances mathematical rigor with practical applicability. It uses just six parameters to capture a wide variety of yield curve shapes — upward sloping, inverted, humped and even more complex forms. In this tutorial, I’ll guide you step-by-step through implementing the NSS model entirely in Python. We’ll go from understanding the underlying math to fetching real market data, coding the model, finding the best parameters and visualizing the results.

Table of Contents

• Mathematical Foundations of the NSS Model: Deconstructing the six-parameter formula and understanding what each parameter means…