Semi-robust static Hedging of Barrier Options

Abstract

We explore how to put the theory on static hedges of barrier options into use. We discuss a polynomial expansion of the exact static hedge in a stationary diffusion model provided by [9] and we develop an explicit expression of an asymptotic static hedge, which is constructed to perform well for short maturities. We derive a semi-robust static hedge in a sense, that it is model independent and depends upon one's beliefs about the future values of implied volatility only.