How does private information get incorporated into option prices? To study this question, I develop a non-linear, noisy rational expectations equilibrium model with asymmetric information and a full menu of call and put options available for trading. The model allows for an arbitrary distribution of the underlying payoff and general trader preferences. All equilibrium prices and portfolios are obtained in closed form. Learning from option prices is characterized explicitly in terms of a novel object, the second derivative of the signal-to-noise ratio, whose sign determines whether particular shapes of option prices are "good news". I show that there is a major difference in equilibrium behaviour for constant absolute risk aversion (CARA) and non-CARA preferences due to feedback effects between wealth, price discovery, and private information: First, if informed traders have non-CARA preferences, strong-form efficiency is always obtained, independent of the amount of noise trading. Second, when informed traders have CARA preferences, the nature of equilibrium changes drastically with wealth effects of uninformed trading: If the latter have non-CARA preferences, weak-form efficiency fails and option prices are not sufficient to recover the information contained in the aggregate demand.