Before revision: We establish an explicit pricing formula for a class of non-Gaussian models (the Levy-stable, or Log-Levy model with finite moments and stability parameter between 1 and 2) allowing a straightforward evaluation of an European option , without numerical simulations and with as much accuracy as one wishes .
After revision: We establish an explicit pricing formula for a class of non-Gaussian models (the Levy-stable, or Log-Levy model with finite moments and stability parameter between 1 <\alpha\leq 2) allowing a straightforward evaluation of an European option , without numerical simulations and with as much accuracy as one wishes .