Numerical Methods For Bermudan Option Pricing

The essence of an option is a kind of right,which means that the option buyer can choose to purchase or sell an asset at a certain fixed price within the trading time.When the option buyer waives the exercise of power,option will become a piece of waste paper.Bermudan option is a special exotic option,which allows the holder to choose whether exercise or not at a limited specific time(for example,every Sunday of the month).Because of its special construction,the valuation is not trivial.In this thesis,we derive the partial differential equation model for Bermudan option under the framework of Black-Scholes theory.Then,we transform the original infinite boundary nonlinear problem to a truncated region problem.Furthermore,we introduce two numerical methods to solve the constructed model: Finite Difference Method and Finite Element Method.The error analysis of these numerical methods are presented.Finally,we verify the validity of the numerical method by numerical experiments.