Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani

We investigate pricing issue of discrete-double barrier options under Lévy processes. We first derive an analytical pricing formula, which is no longer applicable when the monitoring frequency becomes large. Therefore, we present a numerical algorithm based on the idea of using discrete variables to approximate continuous ones initiated by Milev and Tagliani (2010) and utilizing adaptive Gauss-Lobatto quadrature with five points to address the integration problem. The method applies for all types of Lévy processes whose probability density function of the increment is available in closed form. Numerical experiments confirm that our algorithm is both effective and efficient.