On a Black–Scholes American Call Option Model

Morteza Garshasbi () and Shadi Malek Bagomghaleh ()
Additional contact information
Morteza Garshasbi: Iran University of Science and Technology
Shadi Malek Bagomghaleh: Iran University of Science and Technology

Computational Economics, 2025, vol. 65, issue 4, No 14, 2179-2204

Abstract: Abstract This study focuses on the Black–Scholes American call option model as a moving boundary problem. Using a front-fixing approach, the model is derived as a fixed domain nonlinear parabolic problem, and the uniqueness of both the call option price and critical stock price is established. An iterative approach is established to numerically solve the problem, and the convergence of the iterative method is proved. For computational implementation, a finite difference scheme in conjunction with a second-order Runge–Kutta method is conducted. Finally, the numerical results for two test problems are reported in order to confirm our theoretical achievements.

Keywords: Black–Scholes model; American call option; Critical stock price; Uniqueness; Convergence analysis; 35K55; 74S30; 91B24 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10614-024-10623-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:compec:v:65:y:2025:i:4:d:10.1007_s10614-024-10623-3

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2

DOI: 10.1007/s10614-024-10623-3

Access Statistics for this article

Computational Economics is currently edited by Hans Amman

More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().