Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/239212 
Year of Publication: 
2020
Citation: 
[Journal:] Journal of Risk and Financial Management [ISSN:] 1911-8074 [Volume:] 13 [Issue:] 6 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-22
Publisher: 
MDPI, Basel
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.
Subjects: 
American Options
PDE option pricing
Penalty term
projected SOR
penalization strategy
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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