Discrete LIBOR Market Model Analogy

Abstract: This paper provides a discrete time LIBOR analog, which can be used for arbitrage-free discretization of Levy LIBOR models or discrete approximation of continuous time LIBOR market models. Using the work of Eberlein and Oezkan as an inspiration, we build a discrete forward LIBOR market model by starting with a discrete exponential martingale. We take this pure jump process and calculate the appropriate measure change between the forward measures. Next we prove weak convergence of the discrete analog to the continuous time LIBOR model, provided the driving process converges weakly to the continuous time one and the driving processes are PII's. This especially implies the weak convergence of the model to a Levy LIBOR market model if the driving process variables are infinitely divisible distributions. This also relates our model to an Euler discretization.