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

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 gi...

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Bibliographic Details
Published in:Egyptian Journal of Basic and Applied Sciences Vol. 1; no. 3-4; pp. 177 - 183
Main Authors: Kumar, Sunil, Kumar, Devendra, Singh, Jagdev
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2014
Taylor & Francis
Subjects:
2010
34A08
35A20
Analytical solution
Black-Scholes equation
European option pricing
Fractional derivatives
Homotopy analysis method
Homotopy perturbation method
Mathematics Subject Classification
European option pricing
Black–Scholes equation
Homotopy analysis method
Homotopy perturbation method
35A20
Fractional derivatives
Analytical solution
34A08
ISSN:2314-808X, 2314-808X
Online Access:Get full text
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Summary: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. •We consider a fractional model of Black–Scholes equation.•The HPM and HAM are applied to obtain the solution of the problem.•The results obtained by HPM and HAM are in excellent agreement.•The numerical results show that the techniques are easy to implement and accurate.
ISSN:2314-808X
2314-808X
DOI:10.1016/j.ejbas.2014.10.003