South African Government Bond Yields and the Specifications of Affine Term Structure Models

This study adopts the affine term structure three-factor models outlined by \cite{dai2000specification}, aiming to analyse South African (SA) government bond yields across various maturities. The primary objective is to evaluate whether these models offer robust pricing capabilities—being both admissible and flexible—while capturing the conditional correlations and volatilities of yield factors specific to SA bond yields. For a model to be considered admissible, it must also demonstrate economic identification and maximal flexibility. We thus investigate the short-, medium-, and long-term dynamics of bond yields concurrently. Model estimation involves deriving joint conditional densities through the inversion of the Fourier transform applied to the characteristic function of the state variables. This enables the use of maximum likelihood estimation as an efficient method. We assume that the market prices of risk are proportional to the volatilities of the state variables. The analysis reveals negative correlations between factors. Among the models tested, the $A_1(3)$ model outperforms the $A_2(3)$ model in terms of fit, both in-sample and out-of-sample.