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

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.

KEYWORDS:

• Nonlinear PDE
• free boundary
• transformation
• finite difference methods
• Newton-likemethod
• alternating direction explicit method

2010 AMS SUBJECT CLASSIFICATIONS:

• 60G40
• 65N06
• 65N12

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

V.N. Egorova http://orcid.org/0000-0002-3024-3033

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.