A study of some popular analytical approximation approaches applied to options pricing

Options are financial derivative securities that are widely traded on many exchanges around the world. Indeed options trading forms an essential component in the portfolio management of many financial companies. In particular, American options form the bulk of options traded on exchanges. However, due to the early-exercise feature of American options, pricing such an option involves determining an unknown optimal exercise boundary (OEB), leading to a very nonlinear problem. Many numerical methods and approximation methods have been used to approximate the American option pricing problem. As many numerical methods often require lengthy computational time, fast and accurate analytical approximation methods are in great need. The motivation of this thesis is to explore analytical approximation methods in order to achieve accurate values both efficiently and reliably.