Ninth MSUUAB Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 20 (2013), pp. 7991.
Stabilized Adams type method with a block extension for the
valuation of options
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 byproducts
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
nondividendpaying stock by solving a system resulting from the
semidiscretization of the BlackScholes 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 BlackScholes 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


Dong Y. Nyonna
Department of Accounting, Finance, and Economics
Austin Peay State University
Clarksville, TN 37044, USA
email: NyonnaD@apsu.edu


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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