Affine Short Rate Models

We give a complete characterization of affine term structure (ATS) models based on a general non-negative Markov short rate process. This applies to the classical Cox—Ingersoll—Ross (CIR) model but includes as well short rate processes with jumps. We provide a link to the theory of branching processes and show how CBI-processes naturally enter the field of term structure modelling. Using Markov semigroup theory we exploit the full structure behind an ATS and provide a deeper understanding of some well-known properties of the CIR model. As a byproduct we get that any conservative CBI-process is a semimartingale.