Quasi self-dual processes, with a view on hedging (Thorsten Rheinländer)
Recently semi-static hedging of barrier options has received much attention since it allows to replicate the payo¤ of a path-dependent option by purchasing a non-vanilla European option at the hitting time of the barrier. This method, however, requires a certain quasi self-dual (QSD) property of the underlying asset price process to hold. We aim to characterize QSD processes in the framework of both continuous martingales as well as exponential Lévy processes. In the former case, in particular we extend recent work by M. Tehranchi to characterize Ocone martingales in terms of certain associated stochastic exponentials. In the latter case, we derive new conditions for QSD building up on work by I. Molchanov and M. Schmutz, and show that QSD holds for many popular classes of Lévy models. This is joint work with Michael Schmutz, Universität zu Bern.