Regime-Switching Affine Term Structure Models with Jumps: Evidence from the South African Bond Yields

We present a unified framework for modeling the term structure of interest rates using both the affine term structure models (ATSM) with jumps and regime-switches. The novelty lies in combining affine jump diffusion models with regime-switching dynamics within a unified framework, allowing for state-dependent jump behavior while preserving analytical tractability. This integration enables the model to simultaneously capture nonlinear market regimes and discontinuous movements in interest rates—features that traditional affine models or regime-switching models alone cannot jointly represent. Estimation is carried out using the unscented Kalman filter (UKF) with the believe that it is capable of handling nonlinearity, therefore should estimate the non-Gaussian dynamics well. The yield curve fitting demonstrate that both models fit our data well. RMSEs show that the regime-switching affine jump diffusion (RS-AJD) models outperforms the affine jump diffusion (AJD) in-sample.