A product integration method for the approximation of the early exercise boundary in the American option pricing problem

摘要

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.