Valuing American options under the CEV model by Laplace–Carson transforms

This paper investigates American option pricing under the constant elasticity of variance (CEV) model. Taking the Laplace–Carson transform (LCT) to the corresponding free-boundary problem enables the determination of the optimal early exercise boundary to be separated from the valuation procedure. Specifically, a functional equation for the LCT of the early exercise boundary is obtained. By applying Gaussian quadrature formulas, an efficient method is developed to compute the early exercise boundary, American option price and Greeks under the CEV model.