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Moving boundary transformation for American call options with transaction cost: finite difference methods and computing

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Pages 345-362 | Received 28 Apr 2015, Accepted 06 Oct 2015, Published online: 08 Dec 2015
 

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.

2010 AMS SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially supported by the European Union in the FP7- PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economía y Competitividad Spanish grant MTM2013-41765-P.

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