Static Replication of Barrier Options: Some General Results

Abstract

This paper presents a number of new theoretical results for replication of barrier options through a static portfolio of European put and call options. Our results are valid for options with completely general knock-out/knock-in sets, and allow for time- and state-dependent volatility as well as discontinuous asset dynamics. We illustrate the theory with numerical examples and discuss the practical implementation.

JEL Classification: G12, G13