The method of fundamental solutions for solving options pricing models

• Published in: Applied mathematics and computation 2006-10, Vol.181 (1), p.390-401
• Main Authors: Tsai, C.C., Young, D.L., Chiang, J.H., Lo, D.C.
• Format: Article
• Language: English
• Subjects: American options; Applications; Applied sciences; Artificial boundary conditions; Black–Scholes equations; Exact sciences and technology; Free boundary conditions; Insurance, economics, finance; Mathematics; Method of fundamental solutions; Operational research and scientific management; Operational research. Management science; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic analysis
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.01.046

This paper provides a foundation of the method of fundamental solutions (MFS) for the Options Pricing models governed by the Black–Scholes equation in which both the European option and American options are considered. In the solution procedure, no artificial boundary conditions are imposed for both datum and infinite sides of the stock prices. In the cases of the European options, no time marching procedures are required and numerical results are verified with the exact solutions. Since the free boundary conditions are considered for the American options, boundary update procedure is thus applied. At the same time, numerical results are compared with the results in the literatures. These numerical results indicate the MFS is an effective and robust meshless numerical solution for solving the Options Pricing models.