American lookback options: Early exercise

Lookback options are path dependent contingent claims whose payoff depend on the extrema of a given security's price over a given period. Some of these options are already traded on specialized markets (such as foreign exchange) and mostly in over-the-counter market alongside with other path dependent options (knock-ins, knock-outs, etc.). This thesis examines the existing pricing models of conventional options as well as standard European lookback options and provides some results about early exercise of their American counterparts with the use of notions from the theory of optimal stopping.