Egorova, V.N., Tan, S. H., Lai, Ci-H. ORCID: https://orcid.org/0000-0002-7558-6398, Company, R. and Jodar, L. (2015) Moving boundary transformation for American call options with transaction cost: Finite difference methods and computing. International Journal of Computer Mathematics, 94 (2). pp. 345-362. ISSN 0020-7160 (Print), 1029-0265 (Online) (doi:10.1080/00207160.2015.1108409)

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Abstract

The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden’s and Schubert’s methods are applied as a modification to Newton’s method in the case of nonlinearity in the equation. An alternating direction explicit method with second-order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods.

Item Type:	Article
Additional Information:	This is an Accepted Manuscript of an article published by Taylor & Francis Group in International Journal of Computer Mathematics, in Dec 2015, available online: http://www.tandfonline.com/10.1080/00207160.2015.1108409
Uncontrolled Keywords:	Nonlinear PDE, Free boundary, Transformation, Finite difference methods, Newton-like method, Alternating direction explicit method
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS) Faculty of Engineering & Science
Last Modified:	04 Mar 2022 13:07
URI:	https://gala.gre.ac.uk/id/eprint/14893

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