A Probabilistic Monte Carlo model for pricing discrete barrier options

Abstract

We present an original Probabilistic Monte Carlo (PMC) model for pricing European discrete barrier options. Based on Monte Carlo simulation, 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 without barrier and to which we have applied a filter. We test the consistency of our model with an analytical solution (Merton 1973 and Reiner & Rubinstein 1991) adjusted for discretization by Broadie et al. (1997) and a naïve numerical model using Monte Carlo simulation presented by Clewlow & Strickland (2000). We show that the PMC model accurately price barrier equity options. Market participants in need of selecting a reliable and simple numerical method for pricing discrete barrier options will find our paper appealing. Moreover, the idea behind the method is so elementary that it can be applied to the pricing of complex derivatives involving barriers, easing the valuation step significantly.

Keywords: Monte Carlo Simulation, Option Pricing; Discrete Barrier Options