  We derive a recursive formula for arithmetic Asian option prices with finite
observation times in semimartingale models. The method is based on the
relationship between the risk-neutral expectation of the quadratic variation of
the return process and European option prices. The computation of arithmetic
Asian option prices is straightforward whenever European option prices are
available. Applications with numerical results under the Black-Scholes
framework and the exponential L\'evy model are proposed.
