  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. Each of the element in this
sequence solves a parabolic partial differen- tial 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.
