Options as one of the most important financial derivatives that help investors to hedge investment risk or avoid market risks. And for pricing, the options researchers have worked for decades, some main pricing methods are usually adept into the real market. In this thesis, we will focus on the Asian option which underlying the asset without dividend. In Section 1, We have introduced options and stock prices. Based on the detailed knowledge, the BSM model has been carefully introduced as well as the foundation theorem Itô’s formula. The last part of Section 1 is mainly focused on the derivation of the BSM model for the European option that provides basic equations for the Asian one.