Numerical computation of fractional Black–Scholes equation arising in financial market

Publication date: Available online 15 November 2014 Source:Egyptian Journal of Basic and Applied Sciences Author(s): Sunil Kumar , Devendra Kumar , Jagdev Singh The aim of present paper is to present a numerical algorithm for time-fractional Black–Scholes equation with boundary condition for a European option problem by using homotopy perturbation method and homotopy analysis method. The fractional derivative is described in the Caputo sense. The methods give an analytic solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The methods show improvements over existing analytical techniques. Two examples are given and show that the homotopy perturbation method and homotopy analysis method are very effective and convenient overcomes the difficulty of traditional methods. The numerical results show that the approaches are easy to implement and accurate when applied to time-fractional Black–Scholes equation.

Source: Egyptian Journal of Basic and Applied Sciences - November 15, 2014 Category: Science Source Type: research