Enhanced Numerical Methods for Options with Barriers

Abstract

Most real-world barrier option values have no analytic solutions, either because the barrier structure is complex or because of volatility skews in the market. Numerical solutions are therefore a necessity, but options with barriers are notoriously difficult to value numerically on binomial or multinomial trees or on finite-difference lattices. Their values converge very slowly as the number of tree or lattice levels increases, often requiring unattainably large computing times for even modest accuracy. This article analyzes the biases implicit in valuing options with barriers on a lattice and suggests a method for enhancing their numerical solution. This method helps to correct these biases and works well in practice.