Markovian short rates in multidimensional term structure Lévy models

We study a bond market model and the related term structure of interest rates in which the prices of zero coupon bonds are driven by a multidimensional Lévy process. We show that the short rate forms a Markov process if and only if the deterministic forward rate volatility coefficients are decomposed into products of two factors where the factor depending on the maturity time is the same for all components. The proof is based on the analysis of sample path properties of the underlying multidimensional process.