Improved Least Square Monte-Carlo Methods And Applications

This thesis studies the least squares Monte-Carlo methods and its improved algorithm for pricing American options.There are three popular methods for pricing options:binomial methods, finite difference methods, Monte-Carlo methods. This paper focuses on the least square Monte Carlo (LSM) methods and its improved algorithm for pricing American options. Since it has the analytical solutions, the capped option is used to improve the speed of least square Monte-Carlo methods.Firstly, the thesis provides the literature review for the pricing American options, especially for LSM. Secondly, the LSM is introduced in details. Thirdly, the improved LSM is described. Finally, numerical examples and conclusions are provided.