An improved approximate method for solving two-dimensional time-fractional-order Black-Scholes model: a finite difference approach-Reference-Cited by-同舟云学术

An improved approximate method for solving two-dimensional time-fractional-order Black-Scholes model: a finite difference approach

Published:2024 Issue:7 Volume:9 Page:17205-17233
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Prathumwan Din¹,Khonwai Thipsuda²,Phoochalong Narisara²,Chaiya Inthira²,Trachoo Kamonchat²

Affiliation:

1. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

2. Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand

Abstract

<abstract><p>In this paper, we considered the two-dimensional fractional-order Black-Scholes model in the Liouville-Caputo sense. The Black-Scholes model was an important tool in the financial market, used for determining option prices in the European-style market. However, finding a closed-form analytical solution for the fractional-order partial differential equation was challenging. To address this, we introduced an improved finite difference method for approximating the solution of the two-dimensional fractional-order Black-Scholes model in the Liouville-Caputo sense, based on the Crank-Nicolson finite difference method. This method combined the concepts of the finite difference method for solving the multidimensional Black-Scholes model and the finite difference method for solving the fractional-order heat equation. We analyzed the conditional stability and the order of convergence. Furthermore, numerical examples were provided to illustrate the determination of option prices.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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