Samuel N. Jator, Dong Y. Nyonna, Andrew D. Kerr
Abstract:
We construct a continuous stabilized Adams type method (CSAM) that
is defined for all values of the independent variable on the range
of interest. This continuous scheme has the ability to provide a
continuous solution between all the grid points with a uniform
accuracy comparable to that obtained at the grid points. Hence,
discrete schemes which are recovered from the CSAM as by-products
are combined to form a stabilized block Adams type method (SBAM).
The SBAM is then extended on the entire interval and applied as a
single block matrix equation for the valuation of options on a
non-dividend-paying stock by solving a system resulting from the
semi-discretization of the Black-Scholes model. The stability of the
SBAM is discussed and the convergence of the block extension of the
SBAM is given. A numerical example is given to show the accuracy of
the method.
Published October 31, 2013.
Math Subject Classifications: 65L05, 65L06.
Key Words: Stabilized Adams method; extended block; options;
\hfill\break\indent Black-Scholes partial differential equation.
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Samuel N. Jator Department of Mathematics and Statistics Austin Peay State University Clarksville, TN 37044, USA email: Jators@apsu.edu |
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Dong Y. Nyonna Department of Accounting, Finance, and Economics Austin Peay State University Clarksville, TN 37044, USA email: NyonnaD@apsu.edu |
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Andrew D. Kerr Department of Physics and Astronomy Austin Peay State University Clarksville, Clarksville, TN 37044 email: akerr@my.apsu.edu |
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