Pricing Parisan Options

Abstract

A practical problem with barrier options is the one-touch nature of the knock-in or knock-out provision that is triggered if the barrier is ever reached, however briefly. The contract9s payoff can be greatly affected by sharp but economically unimportant price spikes and outliers, and there is also an incentive for market manipulation near the barrier to push the asset price one way or the other. The Parisian variant of the contract reduces this problem by requiring the barrier to be breached for a specific time period. In this standard contract, the “clock” is reset if the barrier is recrossed before the required period is achieved; a related instrument, dubbed a “Parisian” option by the authors, does not reset the clock each time the barrier is hit, so that barrier crossing time cumulates over multiple excursions. This article describes these interesting contracts and presents a procedure for valuing them.

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