Numerical Solution of European Put Option for Black-Scholes Model Using Keller Box Method
DOI:
https://doi.org/10.25077/jmua.13.3.188-197.2024Keywords:
Black-Scholes model, European put option, Keller-box method, option pricing, Von Neumann stabilityAbstract
In this study, we propose to determine option pricing by using Black-Scholes model numerically. The Keller box method, a numerical method with a box-shaped implicit scheme, is chosen to solve the problem of pricing stock options, especially European-put option. This option pricing involves several parameters such as stock price volatility, risk-free interest rate and strike price. The numerical stability of the method is checked using Von Neumann stability before the simulation is conducted. The influence of interest rates, volatility, and strike price on the option price state that the higher the value of the interest rate parameter, the lower the option price value, while the greater the value of stock price volatility and strike price, the higher the option price.
Downloads
References
Black, F., Scholes, M., 1973, The pricing of options and corporate liabilities, Journal of Political Economy, 81 : 637 – 654
Merton, R.C., 1973, Theory of rational option pricing, The Bell Journal of Political Economy and Management, 1 : 141 – 183
Bohner, M., Zheng, Y., 2009, On analytical solutions of the Black–Scholes equation, Applied Mathematics Letters, 22 : 309 – 313
Rodriguez, S., Marin, F., 2011, European Call option pricing by the Adomian decomposition method, Advances in Dynamical Systems and Applications, 9 : 75 – 85
Trachoo, K., Sawangtong, W., Sawangtong, P., 2017, Laplace transform homotopy perturbation method for the two dimensional
Black Scholes model with European call option, Mathematical and Computational Applications, 22 : 23
Putri, E.R.M., Mardianto, L., Hakam, A., Imron, C., Susanto, H., 2021, Removing non-smoothness in solving Black-Scholes equation using a perturbation method, Physics Letters A, 402 (2021), 127367
Edeki, S.O., Ugbebor, O.O., Owoloko, E.A., 2015, Analytical solutions of the Black–Scholes pricing model for european option valuation via a projected differential transformation method, Entropy, 17, : 7510 – 7521
Mardianto, L., Pratama, A.P., Soemarsono, A.R., Hakam A., Putri E.R.M., 2019, Comparison of numerical methods on pricing of European put options, International Journal of Computing Science and Applied Mathematics, 5 : 30 – 34
Goll, C., Rannacher, R., Wollner, W., 2015, The damped Crank–Nicolson time-marching scheme for the adaptive solution of the Black–Scholes equation, Journal of Computational Finance, 18 : 1 – 37
Jamshed, W., Nisar, K.S., 2021, Computational single-phase comparative study of a Williamson nanofluid in a parabolic trough solar collector via the Keller box method, International Journal of Energy Research 45 : 10696 – 10718
Malik, M.Y., Khan, M., Salahuddin, T., Khan, I., 2016, Variable viscosity and MHD flow in Casson fluid with Cattaneo–Christov heat flux model: Using Keller box method, Engineering Science and Technology, an International Journal 19 : 1985 – 1992
Vajravelu, K, Prasad, K.V., 2014, Keller-box method and its application, Vol. 8, Walter de Gruyter GmbH & Co KG, Berlin
Demin, K., 2011, Finite Volume Methods for Option Pricing, Thesis in Halmstad University
Keller, H.B., 1971, A new difference scheme for parabolic problems in Numerical Solution of Partial Differential Equations–II, Academic Press, Maryland
Wilmott, P., 2006, The Best of Wilmott, Vol. 2, John Wiley & sons, Chichester
Downloads
Published
How to Cite
Issue
Section
License
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0). This license allows published content to be freely accessed, shared, redistributed, and adapted for any purpose, including commercial use, provided that the applicable license conditions are followed.
Copyright Holder
The copyright of articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND), in accordance with the journal's stated copyright policy.
Author Rights
Under the CC BY-SA 4.0 license, authors may share, distribute, and reuse their published articles, subject to the applicable license conditions. These rights include:
-
Self-Archiving: Authors may deposit their published articles in institutional repositories, personal websites, or academic platforms.
-
Reuse: Authors may reuse their published work in subsequent publications, research, teaching materials, or other lawful purposes, provided that appropriate attribution is maintained.
-
Distribution: Authors may share and distribute their published articles without requiring additional permission under the terms of the license.
Creative Commons License (CC BY-SA 4.0)
Under the CC BY-SA 4.0 license, users are free to:
-
Share: Copy and redistribute the material in any medium or format.
-
Adapt: Remix, transform, and build upon the material for any purpose, including commercial purposes.
These permissions are subject to the following conditions:
-
Attribution: Users must give appropriate credit to the original author(s), retain relevant copyright notices, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author(s), copyright holder, or journal.
-
ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same CC BY-SA 4.0 license or a compatible license.
-
No Additional Restrictions: Users may not apply legal terms or technological measures that legally restrict others from exercising the rights granted by the license.
For more information about the CC BY-SA 4.0 license, please visit:
https://creativecommons.org/licenses/by-sa/4.0/
Third-Party Content
Third-party materials, including figures, tables, photographs, and illustrations, are covered by the article's CC BY-SA 4.0 license only when their inclusion under that license is authorized.
Materials excluded from the license must be clearly identified with appropriate copyright notices and attribution. Authors are responsible for obtaining any necessary permissions, while users must comply with the applicable licensing terms or permissions when reusing excluded materials.
Copyright and Licensing Information
Copyright and licensing information should be clearly displayed on each published article's landing page and included in the full-text versions (HTML and PDF), where applicable, to ensure transparency regarding copyright ownership and permitted reuse.
