The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense

Panumart Sawangtong, Kamonchat Trachoo, Wannika Sawangtong and Benchawan Wiwattanapataphee
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Panumart Sawangtong: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Kamonchat Trachoo: Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Wannika Sawangtong: Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Benchawan Wiwattanapataphee: School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA 6845, Australia

Mathematics, 2018, vol. 6, issue 8, 1-14

Abstract: It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional derivative. The analytical solution of the proposed model is investigated by the Laplace transform homotopy perturbation method.

Keywords: Black-Scholes model; fractional derivatives; generalized Mittag-Leffer function; Laplace transform homotopy perturbation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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