Yield Curve - Nelson Siegel
Overview
Forward Rate Model
The Nelson Siegel Model assumes the following functional form for the
forward rates
{% f(t) = \alpha_1 + \alpha_2 \; exp[-t/\beta] + \alpha_3 \; \frac{t}{\beta} \; exp[-t/\beta] %}
The corresponding discount rates are given by
{% D(t) = exp[-\alpha_1t - \beta(\alpha_2 + \alpha_3)(1 - e^{-t/\beta}) + \alpha_3 t e^{-t/\beta}] %}
(see
nawalkha)
Fitting to Data
The Nelson Siegel model is nonlinear, and hence cannot be estimated using
a linear regression. The typical way to fit the paramters to data is
to use some form of numeric
optimization.
