Numerical solution of the time fractional Black-Scholes equation using B-spline technique

Tayyaba Akram; Muhammad Abbas; Ahmad Izani Ismail; Shamsul Rijal Muhammad Sabri; Norlida Mohd Noor

doi:10.1063/5.0075288

Numerical solution of the time fractional Black-Scholes equation using B-spline technique

Tayyaba Akram^*
, Muhammad Abbas
, Ahmad Izani Ismail
, Shamsul Rijal Muhammad Sabri
, Norlida Mohd Noor

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

Financial theory can incorporate fractional differential equation, which provides new concepts and methods for theoretical analysis and practical implementations. In this research, a numerical method to solve time fractional Black-Scholes European option pricing model is developed and applied using extended cubic B-spline and Caputo fractional derivative. The numerical and graphical results shows that the option prices from the proposed technique agree well with the analytical solution.

Original language	English
Title of host publication	Proceedings of the International Conference on Mathematical Sciences and Technology 2020, MATHTECH 2020
Subtitle of host publication	Sustainable Development of Mathematics and Mathematics in Sustainability Revolution
Editors	Mohd Shareduwan Mohd Kasihmuddin, Wen Chean Teh, Nur Nadiah Abd Hamid, Siok Kun Sek, Voon Pang Kong, Zhi Lin Chong
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735441668
DOIs	https://doi.org/10.1063/5.0075288
State	Published - 18 Nov 2021
Externally published	Yes
Event	International Conference on Mathematical Sciences and Technology 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution, MATHTECH 2020 - Penang, Malaysia Duration: 8 Dec 2020 → 10 Dec 2020

Publication series

Name	AIP Conference Proceedings
Volume	2423
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Mathematical Sciences and Technology 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution, MATHTECH 2020
Country/Territory	Malaysia
City	Penang
Period	8/12/20 → 10/12/20

Bibliographical note

Publisher Copyright:
© 2021 American Institute of Physics Inc.. All rights reserved.

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1063/5.0075288

Cite this

Akram, T., Abbas, M., Ismail, A. I., Sabri, S. R. M., & Noor, N. M. (2021). Numerical solution of the time fractional Black-Scholes equation using B-spline technique. In M. S. M. Kasihmuddin, W. C. Teh, N. N. A. Hamid, S. K. Sek, V. P. Kong, & Z. L. Chong (Eds.), Proceedings of the International Conference on Mathematical Sciences and Technology 2020, MATHTECH 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution Article 020002 (AIP Conference Proceedings; Vol. 2423). American Institute of Physics Inc.. https://doi.org/10.1063/5.0075288

Akram, Tayyaba ; Abbas, Muhammad ; Ismail, Ahmad Izani et al. / Numerical solution of the time fractional Black-Scholes equation using B-spline technique. Proceedings of the International Conference on Mathematical Sciences and Technology 2020, MATHTECH 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution. editor / Mohd Shareduwan Mohd Kasihmuddin ; Wen Chean Teh ; Nur Nadiah Abd Hamid ; Siok Kun Sek ; Voon Pang Kong ; Zhi Lin Chong. American Institute of Physics Inc., 2021. (AIP Conference Proceedings).

@inproceedings{222dd9dc39044549909ca5e7af127946,

title = "Numerical solution of the time fractional Black-Scholes equation using B-spline technique",

abstract = "Financial theory can incorporate fractional differential equation, which provides new concepts and methods for theoretical analysis and practical implementations. In this research, a numerical method to solve time fractional Black-Scholes European option pricing model is developed and applied using extended cubic B-spline and Caputo fractional derivative. The numerical and graphical results shows that the option prices from the proposed technique agree well with the analytical solution.",

author = "Tayyaba Akram and Muhammad Abbas and Ismail, \{Ahmad Izani\} and Sabri, \{Shamsul Rijal Muhammad\} and Noor, \{Norlida Mohd\}",

note = "Publisher Copyright: {\textcopyright} 2021 American Institute of Physics Inc.. All rights reserved.; International Conference on Mathematical Sciences and Technology 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution, MATHTECH 2020 ; Conference date: 08-12-2020 Through 10-12-2020",

year = "2021",

month = nov,

day = "18",

doi = "10.1063/5.0075288",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Kasihmuddin, \{Mohd Shareduwan Mohd\} and Teh, \{Wen Chean\} and Hamid, \{Nur Nadiah Abd\} and Sek, \{Siok Kun\} and Kong, \{Voon Pang\} and Chong, \{Zhi Lin\}",

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Akram, T, Abbas, M, Ismail, AI, Sabri, SRM & Noor, NM 2021, Numerical solution of the time fractional Black-Scholes equation using B-spline technique. in MSM Kasihmuddin, WC Teh, NNA Hamid, SK Sek, VP Kong & ZL Chong (eds), Proceedings of the International Conference on Mathematical Sciences and Technology 2020, MATHTECH 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution., 020002, AIP Conference Proceedings, vol. 2423, American Institute of Physics Inc., International Conference on Mathematical Sciences and Technology 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution, MATHTECH 2020, Penang, Malaysia, 8/12/20. https://doi.org/10.1063/5.0075288

Numerical solution of the time fractional Black-Scholes equation using B-spline technique. / Akram, Tayyaba; Abbas, Muhammad; Ismail, Ahmad Izani et al.
Proceedings of the International Conference on Mathematical Sciences and Technology 2020, MATHTECH 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution. ed. / Mohd Shareduwan Mohd Kasihmuddin; Wen Chean Teh; Nur Nadiah Abd Hamid; Siok Kun Sek; Voon Pang Kong; Zhi Lin Chong. American Institute of Physics Inc., 2021. 020002 (AIP Conference Proceedings; Vol. 2423).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Akram, Tayyaba

AU - Abbas, Muhammad

AU - Ismail, Ahmad Izani

AU - Sabri, Shamsul Rijal Muhammad

AU - Noor, Norlida Mohd

PY - 2021/11/18

Y1 - 2021/11/18

N2 - Financial theory can incorporate fractional differential equation, which provides new concepts and methods for theoretical analysis and practical implementations. In this research, a numerical method to solve time fractional Black-Scholes European option pricing model is developed and applied using extended cubic B-spline and Caputo fractional derivative. The numerical and graphical results shows that the option prices from the proposed technique agree well with the analytical solution.

AB - Financial theory can incorporate fractional differential equation, which provides new concepts and methods for theoretical analysis and practical implementations. In this research, a numerical method to solve time fractional Black-Scholes European option pricing model is developed and applied using extended cubic B-spline and Caputo fractional derivative. The numerical and graphical results shows that the option prices from the proposed technique agree well with the analytical solution.

UR - https://www.scopus.com/pages/publications/85120570563

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DO - 10.1063/5.0075288

M3 - Conference contribution

AN - SCOPUS:85120570563

T3 - AIP Conference Proceedings

BT - Proceedings of the International Conference on Mathematical Sciences and Technology 2020, MATHTECH 2020

A2 - Kasihmuddin, Mohd Shareduwan Mohd

A2 - Teh, Wen Chean

A2 - Hamid, Nur Nadiah Abd

A2 - Sek, Siok Kun

A2 - Kong, Voon Pang

A2 - Chong, Zhi Lin

PB - American Institute of Physics Inc.

T2 - International Conference on Mathematical Sciences and Technology 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution, MATHTECH 2020

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Akram T, Abbas M, Ismail AI, Sabri SRM, Noor NM. Numerical solution of the time fractional Black-Scholes equation using B-spline technique. In Kasihmuddin MSM, Teh WC, Hamid NNA, Sek SK, Kong VP, Chong ZL, editors, Proceedings of the International Conference on Mathematical Sciences and Technology 2020, MATHTECH 2020: Sustainable Development of Mathematics and Mathematics in Sustainability Revolution. American Institute of Physics Inc. 2021. 020002. (AIP Conference Proceedings). doi: 10.1063/5.0075288

Numerical solution of the time fractional Black-Scholes equation using B-spline technique

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