Pricing American Options with a Non-Constant Penalty Parameter

Anna Clevenhaus, Matthias Ehrhardt, Michael Günther and Daniel Ševčovič
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Anna Clevenhaus: Applied Mathematics & Numerical Analysis Group, University of Wuppertal, 42119 Wuppertal , Germany
Matthias Ehrhardt: Applied Mathematics & Numerical Analysis Group, University of Wuppertal, 42119 Wuppertal , Germany
Michael Günther: Applied Mathematics & Numerical Analysis Group, University of Wuppertal, 42119 Wuppertal , Germany
Daniel Ševčovič: Department of Applied Mathematics and Statistics, Division of Applied Mathematics, Comenius University, 842 48 Bratislava, Slovakia

JRFM, 2020, vol. 13, issue 6, 1-7

Abstract: As the American early exercise results in a free boundary problem, in this article we add a penalty term to obtain a partial differential equation, and we also focus on an improved definition of the penalty term for American options. We replace the constant penalty parameter with a time-dependent function. The novelty and advantage of our approach consists in introducing a bounded, time-dependent penalty function, enabling us to construct an efficient, stable, and adaptive numerical approximation scheme, while in contrast, the existing standard approach to the penalisation of the American put option-free boundary problem involves a constant penalty parameter. To gain insight into the accuracy of our proposed extension, we compare the solution of the extension to standard reference solutions from the literature. This illustrates the improvement of using a penalty function instead of a penalising constant.

Keywords: American Options; PDE option pricing; Penalty term; projected SOR; penalization strategy (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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