Multidimensional Black-Scholes options

Francesco Paolo Esposito

MPRA Paper from University Library of Munich, Germany

Abstract: In this article we propose an extension of the classical Black-Scholes option in a multidimensional setup. The underlying financial asset is a basket of equity stocks on which a general European type option pay$-$off is considered. Using the distributional Fourier transform, we derive a general formal solution and provide a sufficient condition to construct the former explicitly in a fairly rich set of functions. Finally, we develop two derivative options, which are given in closed$-$form: the first option can be expressed as a linear combination of the classical call/put options, while the second one is a new option with multidimensional underlying, nameley a $\chi^2-$option.

Keywords: Black-Scholes model; pricing equation; linear constant coefficients PDE; distributional Fourier transform; plain vanilla option; $\chi^2-$option (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Date: 2010-12-10
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:42821

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