Pricing of index options in incomplete markets

We characterize a set of risk-neutral measures associated with a comprehensive class of risk averse investors. From this set, we show how to construct option price bounds and recover the implied gamma: a parameter uniquely identifying the marginal investor pricing a given option. Empirically, we find that S&P 500 option prices are reconciled by heterogeneous marginal investors who differ in their assessment of tail risk. This heterogeneity is time-varying, decreases during financial crises, and provides novel insights into the skew patterns of index options. The recovered investors' preferences related to compensation for downside risk help predict future market returns. (C) 2021 Elsevier B.V. All rights reserved.