Multi-Asset Option Pricing with Exponential L\'evy Processes and the Mellin Transform

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.