This paper shows how to decompose the dollar profit earned from an option into two basic components: 1) mispricing of the option relative to the asset at the time of purchase, and 2) profit from subsequent fortuitous changes or mispricing of the underlying asset. This separation hinges on measuring the "true relative value" of the option from its realized payoff. The payoff from any one option has a huge standard error about this value which can be reduced by averaging the payoff from several independent option positions. It appears from simulations that 95% reductions in standard errors can be further achieved by using the payoff of a dynamic replicating portfolio as a Monte Carlo control variate. In addition, it is shown that these low standard errors are robust to discrete rather than continuous dynamic replication and to the likely degree of misspecification of the benchmark formula used to implement the replication.
