A Probabilistic Monte Carlo model for pricing discrete barrier and compound real options

Abstract

PhD, is Associate Professor of Finance at the Telfer School of Management, University of Ottawa. His research interests focus on the problems of measurement errors, specification errors and endogeneity in financial models of returns. He is also interested in developing new methods for forecasting financial time series, especially with regard to hedge fund risk. He has published several books and many articles on quantitative finance and financial econometrics.Correspondence: Pierre Rostan, Department of Management, American University in Cairo, AUC Avenue, P.O. Box 74, New Cairo 11835, Egypt E-mail: prostan@aucegypt.edu ABSTRACT We present an original Probabilistic Monte Carlo (PMC) model for pricing European discrete barrier options and compound real options. On the basis of Monte Carlo (MC) simulation, for barrier options the PMC model computes the probability of not crossing the barrier for knock-out options and crossing the barrier for knock-in options. This probability is then multiplied by an average sample discounted payoff of a plain vanilla option that has the same inputs as the barrier option but barrier-free, and to which we have applied a filter. We test the consistency of our model with an analytical solution (Merton, 1973;Reiner and Rubinstein, 1991) adjusted for discretization by Broadie et al (1997) and a naïve numerical model using MC simulation presented by Clewlow and Strickland (2000). Our study shows that the PMC model accurately prices barrier options. Moreover, the idea behind the method is simple and can be applied to the pricing of complex derivatives, easing the valuation step significantly: we illustrate the versatility of the PMC model in pricing