Exotic options with Lévy processes: the Markovian approach

This paper proposes a simplified methodology to price exotic options when the log returns follow a Lévy process. The Markovian approach is simpler than others proposed in literature for these processes and it allows to define hedging strategies. In particular, the authors consider three Lévy processes (variance gamma, Meixner and normal inverse Gaussian) and show how to compute barrier, compound and lookback option prices. The article first discusses the use of a homogeneous Markov chain approximating the risk neutral log return distribution. Then, it describes the methodology to price exotic contingent claims. Finally, the paper compares the convergence results considering the three different distributional assumptions.