A product integration method for the approximation of the early exercise boundary in the American option pricing problem. (12th March 2019)

• Record Type: Journal Article
• Authors: Nedaiasl, Khadijeh; Bastani, Ali Foroush; Rafiee, Aysan
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 8(2019)
• Page Start: 2825
• Page End: 2841
• Publication Date: 2019-03-12
• Subjects: American options pricing -- barycentric rational interpolation -- early exercise boundary -- interpolatory quadrature -- Volterra integral equations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5553
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Integral equation methods are now becoming well‐established tools in the study of financial models used in theory and practice. In this paper, we investigate the fully nonlinear weakly singular nonstandard Volterra integral equations representing the early exercise boundary of American option contracts, which gained popularity in recent years. We propose a product integration approach based on linear barycentric rational interpolation to solve the problem. The price of the option will then be computed using the obtained approximation of the early exercise boundary and a barycentric rational quadrature. The convergence of the approximation scheme will also be analyzed. Finally, some numerical experiments based on the introduced method are presented and compared with some exiting approaches.