A combinatorial approach for pricing Parisian options

This paper provides a discrete time algorithm, in the framework of the Cox–Ross–Rubinstein analysis (1979), to evaluate both Parisian options with a flat barrier and Parisian options with an exponential boundary. The algorithm is based on a combinatorial tool for counting the number of paths of a particle performing a random walk, that remains beyond a barrier constantly for a period strictly smaller than a pre-specified time interval. As a result, a binomial evaluation model is derived that is very easy to implement and that produces highly accurate prices.