An Integral Equation Approach To Pricing Perpetual Bermudan Options

In recent years, pricing problems for non-standard American options have been increasingly received attention. A perpetual Bermudan option is a kind of non-standard American options which has no maturity and only allows exercise at pre-prescribed times. The research for perpetual Bermudan options pricing now is not rich and some of the existing algorithms are not of high accuracy. Due to characteristics of early exercise, pricing of perpetual Bermudan options is extremely complex. So in practice, the financial engineers often use the early exercise policy for perpetual American options to replace that for perpetual Bermudan options. However, to our best knowledge, there is no literature investigating the validity of such replacement.In this thesis, we develop high-order collocation methods to solve the optimal exercise boundary and the pricing problems for perpetual Bermudan options. By implementing the high-order collocation methods, we obtain more accurate and reliable results and verify the validity of replacing the early exercise policies with perpetual American options, and explore a simplified computational process using the formulas for perpetual American options.Firstly, perpetual Bermudan options, American options and high-order collocation methods are reviewed. Secondly, the integral equations, which characterize the optimal exercise boundary and the price of perpetual Bermudan options, are solved using collocation methods. Finally numerical examples are provided and conclusions are given.