Fractional model and solution for the Black‐Scholes equation

Abstract

This work presents a new model of the fractional Black-Scholes equation by using the right fractional derivatives to model the terminal value problem. Through nondimensionalization and variable replacements, we convert the terminal value problem into an initial value problem for a fractional convection diffusion equation. Then the problem is solved by using the Fourier-Laplace transform. The fundamental solutions of the derived initial value problem are given and simulated and display a slow anomalous diffusion in the fractional case. KEYWORDS asset pricing models, Black-Scholes equation, fractional derivative, initial value problem, mathematical finance, terminal value problem Math Meth Appl Sci. 2018;41 697-704.wileyonlinelibrary.com/journal/mma

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