Pricing Asian Options for Jump Diffusions

We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. We show that each of the element in this sequence is the unique classical solutions of a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accuracy versus speed characteristics can be controlled. We analyze the performance of our numerical algorithm on several examples.