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Pantazopoulos, Konstantinos N.; Houstis, Elias N.; Kortesis, S. K.

doi:10.1023/a:1008695215988

Cited by 13 publications

(1 citation statement)

References 17 publications

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“…Other papers present finite difference methods (see, for example, Hull and White [7], Duffy [8], Wilmott et al [9]). An alternative approach is based on front-tracking methods that keep track of the boundary and discretize the problem in changing domain; they have been considered in [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A Front-Fixing Implicit Finite Difference Method for the American Put Options Model

Fazio

Insana

Jannelli

2021

MCA

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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.

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