Ninth MSU-UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 20 (2013), pp. 79-91.

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 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
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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