In the now-classical real options theory, the price of an underlying asset is modeled as a geometric Brownian motion, and optimal exercise strategies are described by simple explicit formulas. This paper extends the classical theory to allow any geometric Le´vy process to model prices. Such processes may account for fat tails and skewness of probability distributions of commodity prices. The optimal exercise strategies are specified in the paper in terms of statistics of record-setting low or high prices. The formulas derived extend those observed in the Gaussian case, but the form of the result is novel even for that case.