Efficient static replication of European options under exponential Lévy models

Abstract

AbstractThis study proposes a new scheme for the static replication of European options and their portfolios. First, a general approximation formula for efficient static replication as an extension of Carr P. and Chou A. (1997, 2002) and Carr P. and Wu L. (2002) is derived. Second, a concrete procedure for implementing the scheme by applying it to plain vanilla options under exponential Lévy models is presented. Finally, numerical examples in a model developed by Carr, P., Geman, H., Madan, D., and Yor M. (2002) are used to demonstrate that the replication scheme is more efficient and more effective in practice than a standard static replication method. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 29:1–15, 2009