A New Procedure for Pricing Parisian Options

Parisian options extend barrier options in that their covenant depends on the time spent by the underlying beyond a given threshold. Due to their very nature, they are hard to price and hedge, though some quite involved material has been made available in that direction. Valuation of Parisian Options can be done by using four different main methods: Monte- Carlo simulations, lattices, partial differential equations, inverse Laplace transform. In this article, we develop a new inverse Laplace transform method, quick and well-suited to the problem under study. This method could also be used to treat other financial problems where inversion of a Laplace transform is required.