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Valuation of the American put option as a free boundary problem through a high-order difference scheme

  • Murat Sari ORCID logo and Seda Gulen ORCID logo EMAIL logo
Published/Copyright: November 29, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 23 Issue 7-8

Abstract

Valuation of the American options encountered commonly in finance is quite difficult due to the possibility of early exercise alternatives. Since an exact solution for the American options does not exist, effective numerical methods are needed to understand the behavior of option pricing models. Therefore, in this paper, a new approach based on a high-order difference scheme is proposed to discuss the valuation of an American put option as a free boundary problem. Using a front-fixing approach that transforms the unknown free boundary (optimal stopping) into a fixed one, a sixth-order finite difference scheme (FD6) in space and a third-order strong-stability preserving Runge–Kutta (SSPRK3) in time are applied to the model converted to a nonlinear partial differential equation. The computed results revealed that the combined method is seen to attempt to pull up the capacity of the algorithm to achieve higher accuracy. It is seen that the quantitative and qualitative results produced by the method proposed with minimal computational effort are sufficiently accurate and meaningful. Therefore, this article provides some new insights about the physical characteristics of financial problems and such realistic phenomena.

Keywords: American put option; free boundary; front-fixing method; high-order difference
2010 Mathematics Subject Classification: 35Q91; 65M06
Corresponding author: Seda Gulen, Department of Mathematics, Faculty of Arts and Science, Tekirdag Namik Kemal University, Tekirdag, Turkey, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-03-01
Accepted: 2021-09-22
Published Online: 2021-11-29
Published in Print: 2022-12-16

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2020-0252
Keywords for this article
American put option; free boundary; front-fixing method; high-order difference

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Coordinated target tracking in sensor networks by maximizing mutual information
  4. Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties
  5. Computational study of intravenous magnetic drug targeting using implanted magnetizable stent
  6. Extended logistic map for encryption of digital images
  7. Valuation of the American put option as a free boundary problem through a high-order difference scheme
  8. Power minimization of gas transmission network in fully transient state using metaheuristic methods
  9. A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds
  10. Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation
  11. Dynamic characteristics of supersonic turbulent free jets from four types of circular nozzles
  12. New insights into singularity analysis
  13. Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations
  14. Wavelet collocation methods for solving neutral delay differential equations
  15. Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method
  16. Solving nonlinear third-order boundary value problems based-on boundary shape functions
  17. Positive radial solutions for Dirichlet problems involving the mean curvature operator in Minkowski space
  18. Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions
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