In this paper, a new kind of additive process is proposed. Our main goal is to define,
characterize and prove the existence of the LIBOR additive process as a new stochastic process.
This process will be de.ned as a piecewise stationary process with independent increments,
continuous in probability but with discontinuous trajectories, and having "càdlàg" sample paths.
The proposed process is specifically designed to derive interest-rates modelling because it
allows us to introduce a jump-term structure as an increasing sequence of Lévy measures. In
this paper we characterize this process as a Markovian process with an infinitely divisible,
selfsimilar, stable and self-decomposable distribution. Also, we prove that the Lévy-Khintchine
characteristic function and Lévy-Itô decomposition apply to this process. Additionally we
develop a basic framework for density transformations. Finally, we show some examples of
LIBOR additive processes