Title: Basket Option Pricing and the Mellin Transform Manuge, Derek Department of Mathematics and Statistics Mathematics and Statistics Kim, Peter Option pricing has been an increasingly popular area of study over the past four decades. The use of the Mellin transform in such a context, however, has not. In this work we present a general multi-asset option pricing formula in the context of Mellin transforms, extending previously known results. The analytic formula derived computes European, American, and basket options with $n$ underlying assets driven by geometric Brownian motion. Aside from the usual given parameters, the pricing formula requires three components to compute: (i) the Mellin basket payoff function, (ii) the characteristic function (or exponent) of a multivariate Brownian motion with drift, and (iii) the Mellin transform of the early exercise function. A fast discretization is solved, providing option prices at incremental values of initial asset prices. As an application, European put option prices are computed for Canadian bank stocks (n=1) and foreign exchange rates (n=2) with USD denomination. http://hdl.handle.net/10214/7811 2013-12 All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.