Price Discovery for Derivatives

We obtain a basic theory of price discovery across derivative markets with respect to higher-order information, using a model where an agent with general private information regarding state probabilities is allowed to trade arbitrary portfolios of state-contingent claims. In an equivalent options formulation, the informed agent has private information regarding arbitrary aspects of the payoff distribution of an underlying asset and is allowed to trade arbitrary option portfolios. We characterize, in closed form, the informed demand, price impact, and information efficiency of prices. Our results offer a theory of insider trading on higher moments of the underlying payoff as a special case. The informed demand formula prescribes option strategies for trading on any given moment and extends those used in practice for, e.g. volatility trading.