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Alessandra Insana
Department of Mathematics, Computer Science, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres 31, I-98166 Messina, Italy

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Numerical analysis researcher.

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Journal article
Published: 13 April 2021 in Mathematical and Computational Applications
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In this paper, we present an implicit finite difference method for the numerical solution of the Black–Scholes model of American put options without dividend payments. We combine the proposed numerical method by using a front-fixing approach where the option price and the early exercise boundary are computed simultaneously. We study the consistency and prove the stability of the implicit method by fixing the values of the free boundary and of its first derivative. We improve the accuracy of the computed solution via a mesh refinement based on Richardson’s extrapolation. Comparisons with some proposed methods for the American options problem are carried out to validate the obtained numerical results and to show the efficiency of the proposed numerical method. Finally, by using an a posteriori error estimator, we find a suitable computational grid requiring that the computed solution verifies a prefixed error tolerance.

ACS Style

Riccardo Fazio; Alessandra Insana; Alessandra Jannelli. A Front-Fixing Implicit Finite Difference Method for the American Put Options Model. Mathematical and Computational Applications 2021, 26, 30 .

AMA Style

Riccardo Fazio, Alessandra Insana, Alessandra Jannelli. A Front-Fixing Implicit Finite Difference Method for the American Put Options Model. Mathematical and Computational Applications. 2021; 26 (2):30.

Chicago/Turabian Style

Riccardo Fazio; Alessandra Insana; Alessandra Jannelli. 2021. "A Front-Fixing Implicit Finite Difference Method for the American Put Options Model." Mathematical and Computational Applications 26, no. 2: 30.