Ninth MSU-UAB Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 20 (2013), pp. 79-91.
Title: Stabilized Adams type method with a block extension for the
valuation of options
Authors: Samuel N. Jator (Austin Peay State Univ., Clarksville, TN, USA)
Dong Y. Nyonna (Austin Peay State Univ., Clarksville, TN, USA)
Andrew D. Kerr (Austin Peay State Univ., Clarksville, TN, USA)
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;
Black-Scholes partial differential equation.