Markovian short rates in a forward rate model with a general class of Lévy processes

Short rates of interest are considered within in the term structure model of Eberlein-Raible [6] driven by a Lévy process. It is shown that they are Markovian if and only if the volatility function factorizes. This extends results of Caverhill [5] for the Wiener process and of Eberlein, Raible [6] for Lévy processes with a restricting property to the most general class of Lévy processes being possible within this model. As new examples compound Poisson processes and bilateral gamma processes are included, in particular variance gamma processes in the sense of Madan [14], Madan, Senata [15].