An investigation into popular methods for constructing yield curves

Abstract

In this dissertation we survey a variety of methods for constructing zero-coupon yield curves. We show that, when accuracy is of the utmost importance, the bootstrap described by Hagan and West (2006), Smit (2000), and Daeves and Parlar (2000) provides the ideal framework. This bootstrap requires the use of an interpolation algorithm, and a large portion of this dissertation will thus be devoted to the task of establishing an ideal method for interpolating yield curve data. Only two of the interpolation methods considered in this dissertation are seen to perform promisingly: the monotone convex method developed by Hagan and West (2006), and the monotone preserving r(t)t method developed in this dissertation. We show that the monotone preserving r(t)t method performs slightly better than the monotone convex method, in terms of the continuity of the forward curve, and in terms of the stability of the interpolation function. When economic appeal is of the utmost importance, we find parametric models to be more suitable than bootstrapping. However, we show that bootstrapping can be used to obtain a hypothetical set of zero-coupon bond prices, which can be used to calibrate parametric models. We compare the performance of the Nelson and Siegel (1987) and Svensson (1992) models, when applied to a historic set of South African swap curves, and show that the Svensson (1992) model performs better than the Nelson and Siegel (1987) model on a consistent basis. Copyright