We derive a general formula for pricing options with barrier and/or lookback features, which covers several types of options studied in the literature and new types of options, and demonstrate that the pricing formula can be efficiently realized using the methodology developed in Kudryavtsev and...

Motivated by the pricing of first touch digital options in exponential Lévy models and corresponding credit risk applications, we study numerical methods for solving related partial integro-differential equations. The goal of the paper is to consider advantages of the Laplace transform-based...

The paper suggest a new approach to pricing barrier options under pure non-Gaussian Levy processes with jumps of finite variation. The key idea behind the method to represent the process under consideration as a difference between subordinators (increasing Levy processes). Such splitting rule...

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 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...

We describe a numerical method for solving 3-dimensional partial differential equations, which arise in mathematical finance and other applications. The goal of the paper is to introduce a technique based on Wiener-Hopf factorization with application of Laplace transform. We analyze the problem...

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...