Analytical solution of time fractional Black-Scholes equation with two assets through new Sumudu Transform iterative method

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Manzoor Ahmad
Rajshree Mishra
Renu Jain

Abstract

There is a scopious rise in the study of financial derivatives over the past two or three decades. Mathematical model proposed by Black and Scholes expounds financial derivatives in a more momentous way. The Black-Scholes model on a single asset is a partial differential equation characterizing the behavior of European options. In this article, we introduce the new Sumudu transform iterative method (NSTIM) as a new technique to obtain the analytical solution of time fractional Black-Scholes model involving European options with two assets. The proposed model is the advanced version of the regular Black-Scholes model. Explicit solution of the problem has been obtained with the help of generalized Mittag-Leffer function. The numerical analysis prove that this method is efficacious in solving various problems of financial theory.

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How to Cite
Ahmad, M., Mishra, R., & Jain, R. (2023). Analytical solution of time fractional Black-Scholes equation with two assets through new Sumudu Transform iterative method. Gulf Journal of Mathematics, 15(1), 42-56. https://doi.org/10.56947/gjom.v15i1.1060
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