Yield curve fitting: A new methodology

The overall objective of this paper is to introduce a new methodology of fitting zerocoupon yield curves. Toward this end, Chebyshev polynomials are incorporated into a quantity called the interest cumulator and then subjected to a minimisation 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. Several innovations are discerned: (i) the minimisation program based upon the logarithmic norm is found to be superior to the standard form based upon the price norm; (ii) Chebyshev polynomials possess desirable properties that improve the econometrics of yield curve fitting; (iii) the empirical results reveal exceptional goodness of fit; and (iv) to my knowledge these are the first published Australian zero-coupon yield curves.