### Analytical solution of time-fractional N-dimensional Black-Scholes equation using LHPM

Sanjay Ghevariya, CHETANBHAI PATEL

#### Abstract

A famous Black-Scholes differential equation is used for pricing options in financial world which represents financial derivatives more significantly. Option is one of the crucial financial derivatives. Sawangtong P., Trachoo K., Sawangtong W. and Wiwattanapataphee B. obtained analytical solution of Black-Scholes equation with two assets in the Liouville-Caputo time-fractional derivative sense using Laplace homotopy perturbation method (LHPM). The aim of this paper is to derive solution of Liouville-Caputo time-fractional Black-Scholes equation with n assets using LHPM. Numerical results shows that our approach gives very accurate results and our formulas are quite close to the plain vanilla options.

#### Keywords

Financial derivatives, European options, n-dimensional Black-Scholes Equation; Liouville-Caputo Fractional Derivative, Laplace homotopy perturbation method.

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DOI: http://dx.doi.org/10.23755/rm.v48i0.1230

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