BFS 2002

Poster Presentation

A Combinatorial Approach for Pricing Parisian Options

Massimo Costabile

This paper provides a discrete time algorithm, in the framework of the standard binomial pricing model of Cox-Ross-Rubinstein, to evaluate Parisian options. The algorithm is based on a combinatorial tool to count 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. Once we get this number, we use it to develop a binomial pricing model to evaluate Parisian options both with a constant barrier and with an exponential boundary. The algorithm proposed here is very easy to implement and, moreover, numerical results show that it produces highly accurate prices.