Time Fractional Black–Scholes Model and Its Solution Through Sumudu Transform Iterative Method

Manzoor Ahmad (), Rajshree Mishra and Renu Jain
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Manzoor Ahmad: Jiwaji University
Rajshree Mishra: Govt. Model Science College
Renu Jain: Jiwaji University

Computational Economics, 2025, vol. 66, issue 5, No 21, 4199-4218

Abstract: Abstract A fractional Black–Scholes (B–S) model of order $$\gamma $$ γ is obtained when the change is subjected to price under the basic fractal communication system. In this work, we have presented the exact solution of time fractional B–S equations determining European options using a new method known as the Sumudu transform iterative method. The solution is given in a convergent series form demanding no additive assumptions or discretization. Four examples are solved using the proposed method and the Mittag-Leffler function appears in the closed form solutions of these examples. Numerical results prove the accuracy and easy to use approach of the method for solving time fractional B–S equation. At the same time, numerical experiments indicate that the time fractional B–S equation is more competent with the actual financial market scenarios. The prime focus of this study is to minimize the difficulty of computational work related to other conventional methods. Moreover, it is an efficient technique to solve general time fractional order partial differential equations arising in many fields of engineering, economics, physics and numerous other disciplines.

Keywords: Option pricing; European options; Fractional Black–Scholes equation; Sumudu transform iterative method; Caputo fractional derivative; Mittag-Leffler function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10614-025-10853-z

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