  In this work, we study the value of an Asian option in the case of
exponential Levy markets. More specifically, we are interested in the NIG
(normal inverse Gaussian) the VG (variance gamma) models. The exponential Levy
models produce incomplete markets. There are therefore an infinite number of
equivalent martingale measures. We are interested in two methods of
constructing of the risk-neutral measures. The first is based on the Esscher
transform, and the other consists of bringing a risk-neutral correction on the
dynamics of the trajectories. It turns out, according to the numerical results
obtained, that the two methods generally produce the same prices.
