Quarter-Sweep Improving Modified Gauss-Seidel Method for Pricing European Option

Authors

  • W. S. Koh
  • Jumat Sulaiman
  • R. Mail

DOI:

https://doi.org/10.11113/matematika.v26.n.561

Abstract

The aim of this paper is to examine the application of the Quarter-Sweep Improving Modified Gauss-Seidel (QSIMGS) method in evaluating European option which governed by Black-Scholes partial differential equation (PDE). Quarter-sweep Crank-Nicolson approach is applied to approximate the PDE. Then, the generated linear system is solved by using the IMGS method. Some numerical experiments for a family of Gauss-Seidel (GS) methods such as Gauss-Seidel, Modified Gauss-Seidel (MGS) and Improving Modified Gauss-Seidel (IMGS) methods are performed with each full-, half-, and quarter-sweep iterations. Thus, from the numerical results obtained, we can show that the QSIMGS method is the most effective method. Keywords: Quarter-Sweep Improving Modified Gauss-Seidel method; Black-Scholes PDE; Crank-Nicolson scheme.

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Published

2010-12-01

Issue

Section

Mathematics