Index Option Returns and Generalized Entropy Bounds

80 Pages Posted: 21 Sep 2012 Last revised: 5 Sep 2019

See all articles by Yan Liu

Yan Liu

Purdue University; Texas A&M University, Department of Finance

Date Written: September 4, 2019


We develop a new continuum of nonparametric bounds. They stem from the solution of an optimization problem that is complementary to Hansen and Jagannathan's (1991) approach, and are shown to complete the nonparametric bound universe the literature has so far discovered. Through the lens of these bounds, we estimate rare-event distributions using index option returns. We show that standard disaster models and their perturbations are unable to meet the bounds implied by simple static option trading strategies. We also highlight the potential and the necessity of having more sophisticated disaster models to reconcile model moments with the index option data.

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). Available at SSRN: or

Yan Liu (Contact Author)

Purdue University ( email )

West Lafayette, IN 47907-1310
United States


Texas A&M University, Department of Finance ( email )

Wehner 401Q, MS 4353
College Station, TX 77843-4218
United States

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