Pricing of American Lookback Options Using Linear Programming

Abstract

We will introduce the American lookback option in the Black-Scholes model. Afterwards we will examine the process it inherits and derive and formulate the linear program needed to price it. As an approximation, we will apply a time-discretization and a truncation of the innite space. The requirements for a solution are weakened and the optimization problem is reduced to base functions,being linear functions. In the end we study the numerical results following from the above computations.