Pricing Parisian Options

Parisian options are barrier options for which the knock-in/knock-out feature is only activated after the price process has spent a certain prescribed, consecutive time beyond the barrier. This specification has two motivations: First, there is the need to make the option more robust against short-term movements of the share price. This is achieved in Parisian options where it is ensured that a single outlier cannot trigger the barrier. In particular, it is far harder to affect the triggering of the barrier by manipulation of the underlying (see Taleb [4]). Second, classical barrier options present hedging problems close to the barrier because their Gamma becomes very large. To some extent, these problems are reduced, or at least ‘smoothed’, in the Parisian contract.