Interpolating the South African Yield Curve using Principal-Components. Analysis: A Descriptive Approach

A principal-components analysis of the South African yield curve suggests that two factors explain most of the variability in both yields and changes in yields. This result is used to select which two interest rates to model and, given a model for these rates, how to use them to reproduce the entire curve. The objective of this paper is a methodology for interpolating the South African yield curve given a restricted number of yields on that curve, while at the same time minimising the number of yields from which to estimate the remainder of the curve. The interpolated curve can then be used for the purposes of discounting nominal future cash flows. Given values for the selected yields, this methodology provides the best fit to the remainder of the curve in the sense that it minimises the expected root-mean-squared error of the residuals. The paper does not provide a model for the evolution of the yield curve. KEYWORDS Principal components; par yield curve; descriptive yield-curve models; interpolation; South Africa (South African Actuarial Journal: 2002 2: 129-146)