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Journal of Scientific Computing

, Volume 79, Issue 1, pp 517–541 | Cite as

A Local Radial Basis Function Method for Pricing Options Under the Regime Switching Model

  • Hengguang Li
  • Reza MollapouraslEmail author
  • Majid Haghi
Article

Abstract

This paper is devoted to develop an efficient meshfree method based on radial basis functions (RBFs) to solve a system of partial differential equations arising from pricing options under the regime switching model. For global RBF methods, one of the major disadvantages is the computational cost and ill-conditioning associated with the dense linear systems that arise. So, we employ one of the local meshfree methods known as radial basis function based finite difference method. Then with an operator splitting method, sparse and well-conditioned system of complementarity problems are solved very fast for the American option. Also, the uniqueness of solution is proved for the discretized system of equations. Numerical examples presented in the last section illustrate the robustness and practical performance of the proposed algorithm for pricing European and American options.

Keywords

Radial basis functions Finite difference Option pricing Regime switching model 

Notes

Acknowledgements

H. Li was supported in part by the NSF Grant DMS-1819041, and by the Wayne State University Career Development Chair Award.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA
  2. 2.School of MathematicsShahid Rajaee Teacher Training UniversityLavizan, TehranIran
  3. 3.Department of MathematicsOregon State UniversityCorvallisUSA

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