In the first Chapter, a new kind of additive process is proposed. We define, characterize and prove the existence of the LIBOR additive process as a new stochastic process. 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. A no-arbitrage framework to model interest rates with credit risk, based on the LIBOR additive process, and an approach to price corporate bonds in incomplete markets, is presented in the second Chapter. We derive the no-arbitrage conditions under different conditions of recovery, and we obtain new expressions in order to estimate the probabilities of default under risk-neutral measure, and new conditions of weak convergence for price distributions with credit risk. Finally, in the third Chapter, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes.