Index Option Returns and Generalized Entropy Bounds

69 Pages Posted: 21 Sep 2012 Last revised: 7 Jul 2020

Date Written: September 4, 2019


I develop a new spectrum of moment bounds on the pricing kernel. They stem from the solution of an optimization problem that is complementary to Hansen and Jagannathan's (1991) approach. Economically, they measure the discrepancy between what an optimizing agent could achieve if all assets (that are priced by the pricing kernel) were tradable and what she can actually achieve in the real-world market. Through the lens of these bounds, I examine leading macro-finance models using index option returns. I show, in a model-free fashion, the difficulty of several classes of models in meeting option-implied bounds. I highlight the unique information that my bounds
provide compared with existing approaches.

Keywords: High-order moments, Pricing kernel, Rare disasters, Index options, Nonparametric bounds, Model diagnosis

JEL Classification: C10, C14, E21, G11, G12

Suggested Citation

Liu, Yan, Index Option Returns and Generalized Entropy Bounds (September 4, 2019). Journal of Financial Economics (JFE), Forthcoming, Available at SSRN: or

Yan Liu (Contact Author)

Purdue University ( email )

West Lafayette, IN 47907-1310
United States


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