We analyze properties of prices of American options under Levy processes, and the related difficulties for design of accurate and efficient numerical methods for pricing of American options. The case of Levy processes with insignificant diffusion component and jump part of infinite activity but...

We suggest two new fast and accurate methods, Fast Wiener-Hopf method (WHF-method) and Iterative Wiener-Hopf method (IWH-method), for pricing barrier options for a wide class of L'evy processes. Both methods use the Wiener-Hopf factorization and Fast Fourier Transform algorithm. Using an...

We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Gaussian model with the same instantaneous variance. Numerical results are produced to show that for typical parameters values, the relative error of the Gaussian...