This paper shows how to decompose the dollar profitearned from an option into two basic components: i)mispricing of the option relative to the asset atthe time of purchase; and ii) profit from subsequentfortuitous changes or mispricing of the underlyingasset. This separation hinges on measuring the “truerelative value” of the option from its realizedpayoff. The payoff from any one option has a hugestandard error about this value that can be reducedby averaging the payoff from several independentoption positions. Simulations indicate that 95%reductions in standard errors can be furtherachieved by using the payoff of a dynamicreplicating porfolio as a Monte Carlo controlvariate. In addition, the paper shows that these lowstandard errors are robust to discrete rather thancontinuous dynamic replication and to the likelydegree of misspecification of the benchmark formulaused to implement the replication.

Option mispricing profit can be futher decomposed intoprofit due to superior estimation of the volatility(volatility profit) and profitfrom using a superior option valuation formula(formula profit). To make thisdecomposition reiably, the benchmark formula usedfor the attribution needs to be similar to theformula implicitly used by the market to priceoptions. If so, then simulation indicates that thisfurther decomposition can be achieved with lowstandard errors. Basic component ii) can be furtherdecomposed into profit from a forward contract ofthe underlying asset (asset profit)and what I term pure option profit. The asset profitindicates whether the investor was skillful bybuying or selling options on mispriced underlyingassets. However, asset profit could also simply bejust compensation for bearing risk—a distinctionbeyond the scope of this paper. Although simulationindicates that the attrivution procedure gives anunbiased allocation of the option profit to thissource, its standard error is large—a feature commonwith others' attempts to measure performance ofasssets.