A barrier option in which the barrier activation/ deactivation (knock in or knock out) is conditional on the underlying price staying beyond the barrier for a preset consecutive period of time. In other words, the trigger will only be activated or extinguished when the underlying lies outside or inside the barrier for a predetermined period. However, the timer of the excursion time below or above the barrier will be reset when the underlying returns to within the barrier.
The barrier feature has the effect of smoothing the option value and its delta and gamma near the barrier against short-term movements of the underlying price (in fact, gamma in classical barrier options becomes very large when the underlying price is close to the barrier). As a result, this allows for relatively easier hedging. It also makes manipulation of the triggering much harder (some traders manipulate the underlying asset in order to force the cancellation or activation of the option).
This option, which is a crossover between a barrier option and an Asian option, is path-dependent and is usually priced using Monte Carlo simulation or finite-difference solution of a three-dimensional partial differential equation. Generally, Parisian options can be classified as American Parisian options and European Parisian options.
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