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The Nelson-Siegel-[Svensson] Model is a common approach to fit a yield curve. Its popularity might be explained with economic interpretability of its parameters but most likely it is because the European Central Bank uses it. However, what may do for ECB will not necessarily work in all cases: the model parameters are sometimes extremely unstable and fail to converge.
Pitfalls of Nelson-Siegel Yield Curve Modeling - Part I
Pitfalls of Nelson-Siegel Yield Curve Modeling - Part I