Yield Curve Modeling: Nelson-Siegel and Dynamic Models

Module: Fintech AI | Difficulty: Advanced

Nelson-Siegel

Factors

| Factor | Name | Interpretation | |--------|------|---------------| | | Level | Long-term rate | | | Slope | Term premium | | | Curvature | Medium-term |

Dynamic Nelson-Siegel

import numpy as np
from scipy.optimize import curve_fit

class NelsonSiegel:
    def __init__(self):
        self.params = None
    def _ns_curve(self, tau, beta0, beta1, beta2, lam):
        lt = lam * tau
        factor1 = (1 - np.exp(-lt)) / lt
        factor2 = factor1 - np.exp(-lt)
        return beta0 + beta1 * factor1 + beta2 * factor2
    def fit(self, maturities, yields):
        popt, _ = curve_fit(self._ns_curve, maturities, yields,
                          p0=[0.05, -0.02, 0.01, 0.5])
        self.params = popt
    def predict(self, maturities):
        return self._ns_curve(maturities, *self.params)

Research Insight: The Nelson-Siegel model captures the yield curve with just 3-4 parameters. The DNS extension adds dynamics, enabling forecasting. Machine learning improves yield curve modeling by capturing non-linearities and regime changes.