In this paper we study arithmetic Asian options when the underlying stock is driven by special semimartingale processes. We show that the inherently path dependent problem of pricing Asian options can be transformed into a problem without path dependence in the payoff function. We also show that the price satisfies a simpler integro-differential equation in the case that the stock price is driven by a process with independent increments, Lévy processes being a special case. This approach applies for both discretely or continuously sampled options.