Arrow-Debreu Meets Kyle: Price Discovery Across Derivatives

Abstract: We study price discovery in a model where an informed agent has arbitrary private information about state probabilities and trades state-contingent claims. The model unifies the seminal frameworks of Arrow and Debreu (1954) and Kyle (1985). When the claims are options, the informed agent has arbitrary information about the underlying asset's payoff distribution and trades option portfolios. We characterize the informed demand and cross-market information dynamics. Our results provide the first equilibrium-based explanation for longstanding empirical practices and regularities in option markets, such as common trading strategies and the volatility smile across option strikes.