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A product integration method for the approximation of the early exercise boundary in the American option pricing problem
Author(s) -
Nedaiasl Khadijeh,
Bastani Ali Foroush,
Rafiee Aysan
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5553
Subject(s) - barycentric coordinate system , mathematics , quadrature (astronomy) , convergence (economics) , finite difference methods for option pricing , boundary (topology) , interpolation (computer graphics) , numerical integration , valuation of options , mathematical optimization , mathematical analysis , black–scholes model , computer science , econometrics , economics , geometry , volatility (finance) , engineering , economic growth , animation , electrical engineering , computer graphics (images)
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.