Pricing Discrete European Barrier Options Using Lattice Random Walks

Abstract

This paper designs a numerical procedure to price discrete European barrier options in Black-Scholes model. The pricing problem is divided into a series of initial value problems, one for each monitoring time. Each initial value problem is solved by replacing the driving Brownian motion by a lattice random walk. Some results from the theory of Besov spaces show that the convergence rate of lattice methods for initial value problems depends on two factors, namely the smoothness of the initial value (or the value function) and the moments for the increments of the lattice random walk. This fact is used to obtain an efficient method to price discrete European barrier options. Numerical examples and comparisons with other methods are carried out to show that the proposed method yields fast and accurate results.