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A product integration method for the approximation of the early exercise boundary in the American option pricing problem. (English) Zbl 1414.91415

Summary: 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.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
45G05 Singular nonlinear integral equations
65R20 Numerical methods for integral equations
45D05 Volterra integral equations
41A20 Approximation by rational functions
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