Who should buy options (ordinary or "exotic"), and who should sell? Buyers and sellers must differ from the average investor, who will not undertake options positions. We develop a simple binomial model to characterize the expectations (relative to the average or consensus) which must be held by investors to justify buying or selling various types of derivatives, or following dynamic strategies which generate similar payoffs. European option sellers must believe markets are more mean-reverting than average; option buyers must believe they are more mean-averting. The probabilities of ordinary option buyers and sellers are path independent and their expected return process must be a martingale. Path-dependent options or dynamic strategies imply probabilities which are path dependent. "Asian" derivative purchasers must believe the expected return to the underlying asset decreases through time. Lookback purchasers believe the opposite.
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