Lookback options with discrete and partial monitoring of the underlying price

We show that in the world of Black and Scholes (1973) lookback options where the underlying price is monitored discretely instead of continuously can be priced in semi-closed form. We derive pricing formulas for a variety of full and partial lookback options, where monitoring takes place at not necessarily equally-spaced points in time. Analysis of the results shows that monitoring the underlying price discretely instead of continuously may have a significant effect on the prices of lookback options but does not introduce new hedging problems.