Path-Dependent Derivatives

Abstract

Path-dependent derivatives have payoffs that not only depend on the value S _T of the underlying at maturity but also on the values {S _t }_{0 ≤ t ≤ T} attained up to maturity. They can broadly be classified into two categories: weakly and strongly path dependent. The former only depends on the value of the underlying at one or a few instances in time. These points in time might not be known today but can be determined by the future path taken by the underlying. An example is given by the derivative that pays the difference between the maximum value obtained in the time up to maturity and the value at maturity. The maximum only occurs at one instance in time, but viewed from today, we do not know when that will be. In contrast, a strongly path-dependent derivative depends on the whole path.