Numerical Solution for 2D European Option Pricing Using Quarter-Sweep Modified Gauss-Seidel Method
Koh Wei Sin, Jumat Sulaiman and Rasid Mail
DOI : 10.3844/jmssp.2012.129.135
Journal of Mathematics and Statistics
Volume 8, Issue 1
Problem statement: This study presents the numerical solution of two-dimensional European option pricing problem based on Quarter-Sweep Modified Gauss-Seidel (QSMGS) iterative method. In fact, the pricing of European option with two-underlying assets can be governed by two-dimensional Black-Scholes Partial Differential Equation (PDE). Approach: The PDE needs to be discretized by using full-, half- and quarter-sweep second-order Crank-Nicolson schemes to generate a system of linear equations. Then, the Modified Gauss-Seidel, a preconditioned iterative method is applied to solve the generated linear system. Results: In order to examine the effectiveness of QSMGS method, several numerical experiments of Full-Sweep Gauss-Seidel (FSGS), Half-Sweep Gauss-Seidel (HSGS) and Quarter-Sweep Gauss-Seidel (QSGS) methods are also included for comparison purpose. Thus, the numerical experiments show that the QSMGS iterative method is the fastest in computing as well as having the least number of iterations. In the error analysis, QSMGS method shows good and consistent results. Conclusion: Finally, it can be concluded that QSMGS method is superior in increasing the convergence rate.
© 2012 Koh Wei Sin, Jumat Sulaiman and Rasid Mail. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.