Basket Option Pricing and the Mellin Transform

Manuge, Derek
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University of Guelph

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.

basket, European, American, option, Mellin transform, fast Fourier transform, Black-Scholes, multi-asset, geometric Brownian motion