Connecting Discrete and Continuous Path-Dependent Options

This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to external values of the underlying aset. including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an external price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts.