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In this paper, an integral equation representation for the early exerciseboundary of an American option contract is considered. Thus far, a number ofdifferent techniques have been proposed in the literature to obtain a varietyof integral equation forms for the early exercise boundary, all starting fromthe Black-Scholes partial differential equation. We first present a coherentcategorization of exiting integral equation methodologies in the Americanoption pricing literature. In the reminder and based on the fact that the earlyexercise boundary satisfies a fully nonlinear weakly singular non-standardVolterra integral equation, we propose a product integration approach based onlinear barycentric rational interpolation to solve the problem. The price ofthe option will then be computed using the obtained approximation of the earlyexercise boundary and a barycentric rational quadrature. The convergence of theapproximation scheme will also be analyzed. Finally, some numerical experimentsbased on the introduced method are presented and compared to some exitingapproaches.

A Product Integration Method for the Approximation of the Early Exercise Boundary in the American Option Pricing Problem