Multidimensional Black-Scholes options

Esposito, Francesco Paolo (2010): Multidimensional Black-Scholes options.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Black-Scholes model, pricing equation, linear constant coefficients PDE, distributional Fourier transform, plain vanilla option, $\chi^2-$option
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

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