Pricing of Index Options in Incomplete Markets

67 Pages Posted: 22 Mar 2021 Last revised: 10 Jun 2021

See all articles by Caio Almeida

Caio Almeida

Princeton University

Gustavo Freire

Erasmus School of Economics; Tinbergen Institute

Date Written: June 8, 2021


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.

Suggested Citation

Almeida, Caio and Freire, Gustavo, Pricing of Index Options in Incomplete Markets (June 8, 2021). Journal of Financial Economics (JFE), Forthcoming, Available at SSRN: or

Caio Almeida (Contact Author)

Princeton University ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States

Gustavo Freire

Erasmus School of Economics ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA

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