  We derive a series expansion by Hermite polynomials for the price of an
arithmetic Asian option. This series requires the computation of moments and
correlators of the underlying price process, but for a polynomial
jump-diffusion, these are given in closed form, hence no numerical simulation
is required to evaluate the series. This allows, for example, for the explicit
computation of Greeks. The weight function defining the Hermite polynomials is
a Gaussian density with scale $b$. We find that the rate of convergence for the
series depends on $b$, for which we prove a lower bound to guarantee
convergence. Numerical examples show that the series expansion is accurate but
unstable for initial values of the underlying process far from zero, mainly due
to rounding errors.
