Efficient Static Replication of European Options for Exponential Levy Models (Revised in January 2008, Published in “Journal of Futures Markets”, Vol.29-1, 1-15, 2009. )

Abstract

This paper proposes a new scheme for the static replication of European options and their portfolios. First, we derive a general approximation formula for efficient static replication as an extension of Carr and Chou [1997, 2002] and Carr and Wu [2002]. Second, we present a concrete procedure for implementing our scheme by applying it to plain vanilla options under exponential L´evy models. Finally, numerical examples in a model developed by Carr, Geman, Madan and Yor[2002] are used to demonstrate that our replication scheme is more efficient and more effective in practice than a standard static replication method.