Zero-Coupon Yield Curve Estimation: A Principal Component, Polynomial Approach

Polynomial functions of the term to maturity have long been used to provide a general functional form for zero-coupon yield curves. The polynomial form has many advantages over alternative functional forms such as Laguerre, when using non-linear least squares to estimate zero-coupon yield curves with coupon bond data. Most importantly the polynomial form invariably enables convergence of the etimation process. Unfortunately, the simple polynomial form results in estimated models of zero-coupon yield curves that approach either plus or minus infinity as the term increases. This unsatisfactory aspect of the simple polynomial is inconsistent with both theoretical considerations and observational reality. We propose a new zero-coupon yield curve functional form consisting not of simple polynomials of term, tau, but rather constructed from polynomials of 1/(1+tau). This form has the desirable property that long-term yields approach a constant value. Further, we model zero-coupon yields as a linear function of the first k principal components of p polynomials of (1/(1+tau), kThe principal components of poynomials of 1/(1+tau) model is applied to Australian coupon bond data. The results compare favourably to those obtained using the traditional polynomial term model.