LIBOR Interpolation and the HJM Model

Abstract: We follow the lines of Musiela and Rutkowski and extend their interpolation method to models with jumps. Together with an extension method for the tenor structure of a given LIBOR market model (LMM) we get an infinite LIBOR termstructure. Furthermore we present an argument why certain known exponential moment conditions on the HJM Model are necessary. The approach uses finite tenor LIBOR market models as approximation for the HJM model, then extends and interpolates the tenor structure, relating it to the HJM structure.