The Nelson-Siegel-Svensson Yields. Probability Properties and Estimation

Abstract

It is considered the probability properties of the yield interest rates that are generated of Nelson – Siegel (NS) model and the Nelson – Siegel – Svensson (NSS) model. Description of yield models Nelson – Nelson and Siegel – Siegel – Svensson presented as a description of the traditional multi-dimensional affine yield models. It is shown that the model of Nelson – Siegel does not differ from the traditional two-factor affine yield model, volatility of which does not depend on the variables of the market. Accordingly, the model of Nelson – Siegel – Svensson does not differ from a four-factor model. Such description differs from the description of the known representations by F. Diebold and G. Rudebusch by that the dimension of models presented in this paper is reduced by one, that simplifies the calculations. It was found that the latent variables Nelson – Siegel coincide with the state variables of the traditional model. These models give rise to interest rates of the yield to maturity and the forward yields with the normal distribution, for which there found the expectations and covariance matrices explicitly. To estimate the values of the rates of yields to maturity on the current time it is formulated recursive procedure based on the use of the Kalman filter.