Estimation of the term structure of interest rates: an international perspective

The overall objective of this paper is to introduce a new methodology of fitting the term structure of interest rates or zero-coupon yield curves. Toward this end, Chebyshev polynomials are incorporated into a quantity called the interest cumulator and then subjected to a minimization procedure to yield parameters that subsequently maps out zero-coupon yield curves. This methodology is applied to Australian coupon bond data to estimate such yield curves. An international perspective is then provided by a comparison and contrast with international evidence in this area. Several innovations of the paper are discerned: (i) while Chebyshev polynomials are well known in engineering and science, this paper is the first to use it to develop a method to fit zero-coupon yield curves from observed coupon paying bond prices; (ii) the estimation procedure based upon the logarithm norm is found to be superior to the standard form based upon the price norm; (iii) Chebyshev polynomials possess desirable properties that improve the econometrics of yield curve fitting; (iv) the empirical results reveal exceptional goodness of fit; and (v) these results are the first published Australian zero-coupon yield curves.