A transform approach to compute prices and greeks of barrier options driven by a class of Levy processes

In this paper we propose a transform method to compute the prices and greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Levy model with hyper-exponential jumps. Inversion of these single Laplace transform yields rapid, accurate results. These results are employed to construct an approximation of the prices and sensitivities of barrier option...