Valuing american put options using gaussian quadrature

Abstract

In this thesis, American style option``s price is evaluated by two numerical methods, Gaussian quadratue and Chebyshef polynomial approximation. The European option``s is already known as the Black-Scholes formula, which is introduced in this thesis. Gaussian Quadrature is used to evaluate the risk-neutral expectations. And Chebyshev polynomial is used to approximate the option`` value of the next time step which is the integrand in the above problem. In addition, we examine the change in numerical solutions as the order of Gaussian quadrature and Chebyshev polynomial are increased.