A path-dependent option whose payoff, at the time of exercise or expiration, does not depend much on the price events over the course of its life. By nature, path dependent options with weak memory are characterized by its payoff that mainly depends on the underlying price reaching a predetermined level. For example, installment options are weakly path-dependent “contingent claims” as their premium is paid discretely or continuously in installments, (the buyer does not pay it at the time of purchase). Other examples include American options, with early exercise, and barrier options (standard single and double barrier options). In a barrier option, the only major event that determines its outcome is whether or not the barrier has been triggered.