Analytical Models for American Options

This thesis aims to introduce American option pricing using two main approaches. Carr-Madan's approach: Formulating the option call price as the Fourier inverse of its characteristic function in a dividend-free framework allows the price to be computed using the fast Fourier transform algorithm. Barone-Adesi Whaley's approach: The American option price, formulated as the European option, together with an early exercise premium, allows for a quadratic approximation of the premium, resulting in an analytic approximation of the American option price.