Computing exponential moments of the discrete maximum of a Lévy process and lookback options (Q964688)

The authors propose a new highly computationally efficient method to compute exponential moments of the discrete maximum of a Lévy process and to price lookback options. The method is based on the Hilbert transform and the so-called sinc expansion. The method is accurate due to the powerful approximation theory for functions analytic in a horizontal strip containing the real axis in the complex plane. The discretization error decays exponentially according to step size. The resulting discrete approximation can be implemented using Toeplitz matrix-vector multiplication algorithm based on the fast Fourier transform. As to financial applications, the paper focuses on the pricing of European-style discretely monitored floating strike, fixed strike, forward start and partial lookback options in exponential Lévy models.