Abstract
In this paper we propose an explicit finite-difference scheme to solve the American option pricing problem. It is based on front-fixing transformation that involves unknown free boundary to the equation. The proposed stable and consistent numerical scheme preserves positivity and monotonicity of the solution in accordance with the behavior of the exact solution. Numerical examples and comparison with other methods are included. This technique can be applied to some types of two-asset options after reducing the dimension. In the paper the front-fixing method is applied to exchange option pricing.
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Acknowledgements
This paper 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).
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Company, R., Egorova, V.N., Jódar, L. (2016). A Positive, Stable and Consistent Front-Fixing Numerical Scheme for American Options. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. ECMI 2014. Mathematics in Industry(), vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-23413-7_10
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DOI: https://doi.org/10.1007/978-3-319-23413-7_10
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