This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, 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 extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts. We also develop discrete-time discrete-state lattice methods for determining accurate prices of discrete and continuous path-dependent options. In several cases, the lattice methods use correction terms based on the connection between discrete- and continuous-time prices which dramatically improve convergence to the accurate price.
Broadie, Mark, Paul Glasserman, and Shing-Gang Kou. "Connecting Discrete and Continuous Path-Dependent Options." Finance and Stochastics 3, no. 1 (1999): 55-82.
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