A Hybrid Approach to Valuing American Parisian Options

Abstract

We propose a methodology that combines simulation and lattice methods to value American Parisian knock-in and knock-out options. Our methodology uses the observation that once the Parisian condition is met, the exercise strategy of a knock-in option is identical to that of a plain vanilla option. For Parisian knock-outs, early exercise decisions can be based on exercise boundaries of two standard options on the same asset - one with the same strike and maturity as the Parisian option and the other with a strike price equal to the price threshold and maturity equal to the time threshold of the Parisian option.