Exotic Options with Lévy Processes : the Markovian Approach

This paper proposes the markovian approach to price exotic options under Lévy processes. The markovian approach is simpler than the others proposed in literature for these processes and it allows to define hedging strategies. In particular, we consider three Lévy processes (Variance-Gamma, Meixner and Normal Inverse Gaussian) and we show how to compute American, barrier, compound and lookback option prices. We first discuss the use of an homogeneous Markov chain approximating the risk neutral log-return distribution. Then, we describe the methodology to price exotic contingent claims under the three different distributional assumptions and we compare the convergence results.