Fast and accurate pricing of barrier options under Lévy processes

We suggest two new fast and accurate methods, the fast Wiener–Hopf (FWH) method and the iterative Wiener–Hopf (IWH) method, for pricing barrier options for a wide class of Lévy processes. Both methods use the Wiener–Hopf factorization and the fast Fourier transform algorithm. We demonstrate the accuracy and fast convergence of both methods using Monte Carlo simulations and an accurate finite difference scheme, compare our results with those obtained by the Cont–Voltchkova method, and explain the differences in prices near the barrier. The first author is supported, in part, by grant RFBR 09-01-00781.