MATEC Web Conf.
Volume 125, 201721st International Conference on Circuits, Systems, Communications and Computers (CSCC 2017)
|Number of page(s)||6|
|Published online||04 October 2017|
Adaptive algorithm for solution of early exercise boundary problem of American put option implemented in Mathematica
University of West Bohemia, Faculty of Economics, Univerzitni 22, 30614 Pilsen, Czech Republic
* Corresponding author: firstname.lastname@example.org
The paper is focused on American option pricing problem. Assuming non-dividend paying American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise action effect. Next, we discuss financially motivated additive decomposition of American option price into a European option price and another part due to the extra premium required by early exercising the option contract. As the optimal exercise boundary is a free boundary, its determination is coupled with the determination of the option price. Therefore, a closed-form expression of the free boundary is not attainable in general. We discuss in detail a derivation of an asymptotic expression of the early exercise boundary. Finally, we present some numerical results of determination of free boundary based upon this approach. All computations are performed by sw Mathematica, and suitable numerical procedure is discussed in detail, as well.
© The Authors, published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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