Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 89, 2012 - Issue 9: COMPUTATIONAL METHODS FOR PDEs IN FINANCE
Submit an article Journal homepage
412
Views
31
CrossRef citations to date
0
Altmetric
Section B

The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost

M. Yousuf Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi ArabiaCorrespondence[email protected]
,
A. Q.M. Khaliq Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN, 37132-0001, USA
&
B. Kleefeld Institut für Mathematik, Brandenburgische Technische Universität Cottbus, Postfach, 101344, 03013, Cottbus, Germany
Pages 1239-1254 | Received 02 Oct 2011, Accepted 22 Mar 2012, Published online: 22 May 2012

Citations (31)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (5)

M. Yousuf. (2019) High-order time stepping scheme for pricing American option under Bates model. International Journal of Computer Mathematics 96:1, pages 18-32.
Read now
M. Yousuf. (2018) A second-order efficient L-stable numerical method for space fractional reaction–diffusion equations. International Journal of Computer Mathematics 95:6-7, pages 1408-1422.
Read now
O. S. Iyiola, E. O. Asante-Asamani, K. M. Furati, A. Q. M. Khaliq & B. A. Wade. (2018) Efficient time discretization scheme for nonlinear space fractional reaction–diffusion equations. International Journal of Computer Mathematics 95:6-7, pages 1274-1291.
Read now
Khaled M. Furati, M. Yousuf & A. Q. M. Khaliq. (2018) Fourth-order methods for space fractional reaction–diffusion equations with non-smooth data. International Journal of Computer Mathematics 95:6-7, pages 1240-1256.
Read now
M. Yousuf, A.Q.M. Khaliq & R.H. Liu. (2015) Pricing American options under multi-state regime switching with an efficient L- stable method. International Journal of Computer Mathematics 92:12, pages 2530-2550.
Read now

Articles from other publishers (26)

M. Yousuf, K.M. Furati & A.Q.M. Khaliq. (2023) A hybrid fourth order time stepping method for space distributed order nonlinear reaction-diffusion equations. Computers & Mathematics with Applications 151, pages 116-126.
Crossref
M. YOUSUF & A. Q. M. KHALIQ. (2023) PRICING AMERICAN OPTION USING A MODIFIED FRACTIONAL BLACK–SCHOLES MODEL UNDER MULTI-STATE REGIME SWITCHING. International Journal of Theoretical and Applied Finance 26:04n05.
Crossref
Christina C. Christara & Ruining Wu. (2022) Penalty and penalty-like methods for nonlinear HJB PDEs. Applied Mathematics and Computation 425, pages 127015.
Crossref
M. Rezaei, A. R. Yazdanian, A. Ashrafi & S. M. Mahmoudi. (2021) Numerically Pricing Nonlinear Time-Fractional Black–Scholes Equation with Time-Dependent Parameters Under Transaction Costs. Computational Economics 60:1, pages 243-280.
Crossref
Abolfazl Mighani, Ali Foroush Bastani & Seyed-Mohammad-Mahdi Kazemi. (2022) On Multilevel RBF Collocation Based on Operator Newton Iteration to Solve Nonlinear Black–Scholes Equations. Iranian Journal of Science and Technology, Transactions A: Science 46:2, pages 429-449.
Crossref
Juan He, Wei Tu & Aiqing Zhang. (2022) Asymptotic Convergence Analysis and Error Estimate for Black-Scholes Model of Option Pricing. Mathematical Problems in Engineering 2022, pages 1-9.
Crossref
E.O. Asante-Asamani, A. Kleefeld & B.A. Wade. (2020) A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting. Journal of Computational Physics 415, pages 109490.
Crossref
M. Yousuf, K.M. Furati & A.Q.M. Khaliq. (2020) High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction–diffusion equations. Computers & Mathematics with Applications 80:1, pages 204-226.
Crossref
S.S. Alzahrani & A.Q.M. Khaliq. (2019) Fourier spectral exponential time differencing methods for multi-dimensional space-fractional reaction–diffusion equations. Journal of Computational and Applied Mathematics 361, pages 157-175.
Crossref
S.S. Alzahrani & A.Q.M. Khaliq. (2019) High-order time stepping Fourier spectral method for multi-dimensional space-fractional reaction–diffusion equations. Computers & Mathematics with Applications 77:3, pages 615-630.
Crossref
Xiao Liang & Harish Bhatt. (2018) Exponential time differencing schemes for the 3-coupled nonlinear fractional Schrödinger equation. Advances in Difference Equations 2018:1.
Crossref
Kolade M. Owolabi & J.F. Gómez-Aguilar. (2018) Numerical simulations of multilingual competition dynamics with nonlocal derivative. Chaos, Solitons & Fractals 117, pages 175-182.
Crossref
O.S. Iyiola & B.A. Wade. (2018) Exponential integrator methods for systems of non-linear space-fractional models with super-diffusion processes in pattern formation. Computers & Mathematics with Applications 75:10, pages 3719-3736.
Crossref
Muhammad Yousuf. (2018) Numerical solution of systems of partial integral differential equations with application to pricing options. Numerical Methods for Partial Differential Equations 34:3, pages 1033-1052.
Crossref
M. Yousuf, A.Q.M. Khaliq & Salah Alrabeei. (2018) Solving complex PIDE systems for pricing American option under multi-state regime switching jump–diffusion model. Computers & Mathematics with Applications 75:8, pages 2989-3001.
Crossref
Ahmad Golbabai & Ehsan Mohebianfar. (2017) A new method for evaluating options based on multiquadric RBF-FD method. Applied Mathematics and Computation 308, pages 130-141.
Crossref
A. Q. M. Khaliq, X. Liang & K. M. Furati. (2016) A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations. Numerical Algorithms 75:1, pages 147-172.
Crossref
A. Golbabai & E. Mohebianfar. (2016) A New Stable Local Radial Basis Function Approach for Option Pricing. Computational Economics 49:2, pages 271-288.
Crossref
E.O. Asante-Asamani, A.Q.M. Khaliq & B.A. Wade. (2016) A real distinct poles Exponential Time Differencing scheme for reaction–diffusion systems. Journal of Computational and Applied Mathematics 299, pages 24-34.
Crossref
E. O. Asante-Asamani & Bruce A. Wade. (2016) A Dimensional Splitting of ETD Schemes for Reaction-Diffusion Systems. Communications in Computational Physics 19:5, pages 1343-1356.
Crossref
Ran Zhang, Qi Zhang & Haiming Song. (2015) An efficient finite element method for pricing American multi-asset put options. Communications in Nonlinear Science and Numerical Simulation 29:1-3, pages 25-36.
Crossref
Jamal Amani Rad, Kourosh Parand & Saeid Abbasbandy. (2015) Local weak form meshless techniques based on the radial point interpolation (RPI) method and local boundary integral equation (LBIE) method to evaluate European and American options. Communications in Nonlinear Science and Numerical Simulation 22:1-3, pages 1178-1200.
Crossref
A. Golbabai, L. V. Ballestra & D. Ahmadian. (2013) A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options. Computational Economics 44:2, pages 153-173.
Crossref
Xiao Liang, Abdul Q.M. Khaliq & Qin Sheng. (2014) Exponential time differencing Crank–Nicolson method with a quartic spline approximation for nonlinear Schrödinger equations. Applied Mathematics and Computation 235, pages 235-252.
Crossref
Tshilidzi MarwalaTshilidzi Marwala. 2013. Economic Modeling Using Artificial Intelligence Methods. Economic Modeling Using Artificial Intelligence Methods 83 100 .
Shengwu Zhou, Wei Li, Yu Wei & Cui Wen. (2012) A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models. Journal of Applied Mathematics 2012, pages 1-20.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.