Pricing Double-Barrier Options Using the Boundary Element Method

Abstract

A numerical method to price double-barrier options with moving barriers is proposed. Using the so-called Boundary Element Method, an integral representation of the double-barrier option price is derived in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. This system of equations is affected by several kinds of singularities, therefore it is first regularized and then solved using a low-order finite element method based on product integration. Several numerical experiments are carried out showing that the method proposed is extraordinarily fast and accurate, also when the barriers are not differentiable functions. Moreover the numerical algorithm presented in this paper performs significantly better than the finite difference approach.

Keywords: Barrier Option, Double Barrier, Time-Dependent Barrier, Boundary Element Method, Volterra Integral Equations

JEL Classification: C02, C63, G13