Analysis of quadrature methods for pricing discrete barrier options

In the present paper we provide an analysis of a quadrature method combined with an interpolation procedure for the valuation of discrete barrier options. The convergence of the method is proved and the computational cost is found to be linear in the number of monitoring dates and quadratic in the spatial discretization. Moreover, we provide an estimate of the error for a given computational time budget. Finally, we discuss extensively the empirical performance of the method, including the calculation of the delta and gamma coefficients, and we compare the GBM, CEV and variance gamma (VG) stochastic specifications.