On Estimability of Parsimonious Term Structure Models: An Experiment with Three Popular Specifications

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 highly non-linear function of the parameters. This necessary entails using numerical optimization techniques for estimation, which brings to fore the issue of (sensitivity of 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 vector for three popular specifications, namely, Nelson-Siegel (1987), Svensson (1994), and Cox-Ingersoll-Ross (1985). It turns out that given the nature of the objective function, the choice of the starting vector is far from obvious in all three cases. There exist regions in the shape of the objective function in all three 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 which results in the objective function value near the minimum and then assess the sensitivity of the final parameter vector to those (subset of) initial values. The study illustrates the process using a typical trading day’s data.