This paper presents a novel method to price discretely-monitored single- and double-barrier options in Levy process-based models. The method involves a sequential evaluation of Hilbert transforms of the product of the Fourier transform of the value function at the previous barrier monitoring...

We present a fast and accurate method to compute exponential moments of the discretely observed maximum of a Levy process. The method involves a sequential evaluation of Hilbert transforms of expressions involving the characteristic function of the (Esscher transformed) Levy process. It can be...