Bond Pricing Based on Nelson-Siegel Model
——An Analysis of Varied Parameter τ
Introduction
Nelson and Siegel (1987) suggest to fit the forward rate curve at a given date with a
mathematical class of approximating functions. The model precisely reflects the expected
YTM with a flexible yield curve in the Term Structure Theorem. In this paper, we test the
fitness of NS model and try to evaluate how deeply the NS model performs with different
types of bonds via sampling and comparasion. We focus on the effects of parameter τ’
changing to analysis NS model.
Model explanation
The functional form Nelson and Siegel advocate uses Laguerre functions which consist of
the product between a polynomial and an exponential decay term. The three components in
NS model have a clear interpretation for short, medium and long-term components. These
labels are the result of each element’s contribution to the yield curve. Basic model:
Where x is a vector parameter, τ is a time constant and f(t, x) donates forward interest rate
in time t.
By average the equation we get the YTM. Which donated by R(x, t),
Later, in order to run the regression, we use OLS methods to minimize the sum square of
interest rate spread.
That can also be written as this form:
Notice that there are only 4 factors in the final model, which gives a very high flexibility to
the research process.
The model shows the forward and yield curves which have the desirable property of
starting o from an easily computed instantaneous short rate value of β0+β1, t and ff
leveling o at a finite infinite-maturity value of β0, that is constant:ff
