## Application of Gauss-Seidel Method on Refined Financial Matrix for Solution to Partial Differential Equation (PDE) in Finance

Published: 2022-10-15

Page: 666-677

Okechukwu U. Solomon *

Department of Physical Science, Rhema University Aba, Abia State, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

A refined financial matrix using Gauss-Seidel method for pricing American option under the Black-Scholes model is proposed and justified. The bases for a Gauss-Seidel method to price an American Option under the Black-Scholes model depends on the complete understanding of the discretization process, computation of nearest symmetric positive semidefinite matrices from an arbitrary matrix, in the 2-norm and in the Frobenius norm.

Years back, a lot of researchers have applied Gauss-Seidel method in solving system equations.

Hermitian differential-algebraic system etc. This paper presents Gauss-Seidel method for American option valuation under Black-Scholes model, through a drifted financial derivative system, discretized from Black-Scholes financial PDE. Some numerical difficulties are discussed by illustrative example.

Keywords: Financial PDE, stochastic algorithm, drifted financial derivative system, option pricing, central finite difference discretization, gauss-seidel method, symmetric positive semidefinite

#### How to Cite

Solomon, O. U. (2022). Application of Gauss-Seidel Method on Refined Financial Matrix for Solution to Partial Differential Equation (PDE) in Finance. Asian Journal of Pure and Applied Mathematics, 4(1), 666–677. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1678

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