  In this paper we present a new methodology for option pricing. The main idea
consists to represent a generic probability distribution function (PDF) via a
perturbative expansion around a given, simpler, PDF (typically a gaussian
function) by matching moments of increasing order. Because, as shown in
literature, the pricing of path dependent European options can be often reduced
to recursive (or nested) one-dimensional integral calculations, the above
perturbative moment expansion (PME) leads very quickly to excellent numerical
solutions. In this paper, we present the basic ideas of the method and the
relative applications to a variety of contracts, mainly: asian, reverse cliquet
and barrier options. A comparison with other numerical techniques is also
presented.
