Efficient pricing options under regime switching

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations.