Numerical Solution for 2D European Option Pricing Using Quarter-Sweep Modified Gauss-Seidel Method | Science Publications

Journal of Mathematics and Statistics

Koh Wei Sin¹  Rasid Mail¹  Jumat Sulaiman¹ 

关键词: Modified Gauss-Seidel;    quarter-sweep iteration;    two-dimensional Black-Scholes PDE;    Crank-Nicolson scheme;   

DOI  :  10.3844/jmssp.2012.129.135

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown