On estimability of parsimonious term structure models: an experiment with the Nelson–Siegel specification

Abstract

This study addresses operational issues in estimation of parsimonious term structure models. When using price errors, objective function in term structure estimation is a nonlinear function of the model parameters. This necessarily entails using numerical optimization techniques for estimation, which brings to fore the issue of (sensitivity of final results to) the choice of initialization of the optimization routine. This study assesses the sensitivity of the final objective function value and the final parameter vector to the choice of the ‘initial guess’ during the estimation of the popular Nelson–Siegel model. It turns out that there exist regions in the shape of the objective function where a slight change in (seemingly reasonable) initial vector takes one far from optimum. Choice of the (range of) ‘best’ starting vector turns out to be an empirical matter. Grid search is recommended. One must first get to a subset of initial values that results in the objective function value near a minimum and then assess the sensitivity of the final parameter vector to those relevant (subset of) initial values. The study illustrates the process using a typical trading day's data.

Keywords:

• term structure
• estimation
• Nelson–Siegel
• sensitivity analysis

JEL Classifications:

• C52
• E43

Notes

¹ A notable exception is Bolder and Streliski (1999).

² This weighing scheme corrects for the heteroskedasticity problem in the error terms that occurs if the price errors are used instead of yield error (Darbha et al., 2003).

³ Note that this is not conditional on the optimization routine used. A contour plot is just a plot of variation in fval as b ₀ changes.