  In this paper we derive a series expansion for the price of a continuously
sampled arithmetic Asian option in the Black-Scholes setting. The expansion is
based on polynomials that are orthogonal with respect to the log-normal
distribution. All terms in the series are fully explicit and no numerical
integration nor any special functions are involved. We provide sufficient
conditions to guarantee convergence of the series. The moment indeterminacy of
the log-normal distribution introduces an asymptotic bias in the series,
however we show numerically that the bias can safely be ignored in practice.
