Barrier Options Under Lévy Processes: A Simple Short-Cut

Abstract

In this paper we present new pricing formulas for some single barrier style contracts of the European type when the underlying process is driven by an important class of Levy processes, which includes the CGMY model, generalized hyperbolic model and Mexiner model, frequently used in the literature. To achieve this goal we first assume that a symmetry property holds, i.e., we assume that under a change of numeraire the risk neutral distribution does not change, and then we analyze the most realistic asymmetric case.