  Exponential L\'evy processes have been used for modelling financial
derivatives because of their ability to exhibit many empirical features of
markets. Using their multidimensional analogue, a general analytic pricing
formula is obtained, allowing for the direct valuation of multi-asset options
on $n \in \z^+$ risky assets. By providing alternate expressions for
multi-asset option payoffs, the general pricing formula can reduce to many
popular cases, including American basket options which are considered herein.
This work extends previous results of basket options to dimensions $n \geq 3$
and more generally, to payoff functions that satisfy Lipschitz continuity.
